Linear groups (Q5902851)

scientific article; zbMATH DE number 3914578

Language	Label	Description	Also known as
English	Linear groups	scientific article; zbMATH DE number 3914578

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instance of

scholarly article

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title

Linear groups (English)

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zbMATH Open document ID

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Alexander E. Zalesskij

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published in

Journal of Soviet Mathematics

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publication date

1985

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review text

Translation from Itogi Nauki Tekh., Ser. Algebra Topologiya Geom. 21, 135-182 (Russian) (1983; Zbl 0561.20033).

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Mathematics Subject Classification ID

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general linear groups

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subgroups of classical groups

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automorphisms

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generators and relations

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bibliography

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MaRDI profile type

MaRDI publication profile

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cites work

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Automorphisms of the general linear group over a commutative ring not generated by zero-divisors

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Some subgroups of the full linear group

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Determinants in net subgroups

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Net determinant over a local Bezout ring

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Conjugacy of net subgroups of linear groups

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Subnormalizer of net subgroups in the general linear group over a ring

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Parabolic subgroups of the full linear group over a Dedekind ring of arithmetical type

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Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices

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Parabolic subgroups of twisted Chevalley groups over a semilocal ring

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Bruhat decomposition for subgroups containing the group of diagonal matrices

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On subgroups of the unitary group over a semilocal ring

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Parabolic subgroups of Chevalley groups over a commutative ring

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Subgroups of the general symplectic group containing the group of diagonal matrices

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Normal structure of the full linear group over a semilocal ring

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Net subgroups of Chevalley groups. II: Gauss decomposition

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Selection of subspaces with special properties in a Banach space and some properties of quasicomplements

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Q3882584

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THE GROUP OF UNITS OF GOLDIE PRIME RINGS

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Generalized group identities in classical groups

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Invariants of linear groups generated by matrices with two nonunit eigenvalues

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Sylow p-subgroups of the group GL(q)

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Groups of linear fractional transformations generated by three elements

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Roots of unity as nonfree points of the complex plane

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Quadratic modules for CHEVALLEY groups over fields of odd characteristics

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Lower central series and derived series of net subgroups of the general linear group

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Isomorphisms of symplectic groups over skew fields of characteristic different from 2

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SUBGROUPS OF $ GL(n,p)$ CONTAINING $ SL(2,p)$ IN AN IRREDUCIBLE REPRESENTATION OF DEGREE $ n$

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One theorem of Cohn

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Some linear groups with complemented subgroups

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Schur multiplier of a group of elementary matrices of finite order

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Subgroups of the full linear group over the field of quotients of a principal ideal domain

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Ein Sylowsatz für endliche $p$-Untergruppen von $GL(n,Z)$

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Linear groups of finite cohomological dimension

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Linear groups of finite cohomological dimension

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The normal subgroup structure of the infinite general linear group

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The subnormal subgroup structure of the infinite general linear group

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Infinite dimensional linear groups

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GF(2)-Representations of Finite Groups

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Cohomology of subgroups of finite index of 𝑆𝐿(3,𝑍) and 𝑆𝐿(4,𝑍)

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Cohomology of congruence subgroups of $SL(n,Z)$

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2-cohomology of some unitary groups

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Automorphism groufs and subgroups of sl2over division rings

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The congruence subgroup and metaplectic problems for $SL_{n>1}$ of division algebras

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Centralizers of reflections in crystallographic groups

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Euler characteristics and characters of discrete groups

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Groups of integral representation type

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Eine Präsentation der symplektischen Gruppe Sp(4,Z) mit 2 Erzeugenden und 8 definierenden Relationen

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Hall-Higman Type Theorems. III

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Hall-Higman type theorems. V

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Hall-Higman type theorems. VI

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A short proof of a theorem of Suslin-Kopeiko

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On groups containing the projective special linear group

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Permutation groups containing projective special linear groups of the same degree: A problem of Mathieu

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Nonparabolic subgroups of the modular group

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On the construction of non-congruence subgroups

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Maximal normal subgroups of the integral linear group of countable degree

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Finite $p$-periodic quotients of general linear groups

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The isomorphisms of unitary groups over noncommutative domains

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2-transitive and antiflag transitive collineation groups of finite projective spaces

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Finite quaternionic reflection groups

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On non-Hurwitz groups and non-congruence subgroups of the modular group

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The MOD 2 cohomology of the orthogonal groups over a finite field

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Q4128997

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Minimal degree for a permutation representation of a classical group

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Nearly maximal representations for the special linear group

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Matrix groups

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Some subgroups of GL(n,2) generated by involutions. I

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Some subgroups of GL(n,2) generated by involutions. II

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Some subgroups of SL(n,$2^ m)$. I

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Stabilizers of isotropic subspaces in classical groups

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Q4187982

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The irreducible subgroups of PSL$(V_5,q)$, where $q$ is odd

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Irreducible solvable linear groups of odd degree

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Q3947831

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Relations between reflections in the unitary group and Hermitian hyperquadrics in the complex projective space

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Discreteness criteria and high order generators for subgroups of SL(2,R)

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Twisted homological stability for general linear groups

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Interrelations of symplectic and orthogonal groups in characteristic two

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Symmetric Groups as Maximal Subgroups of Orthogonal and Symplectic Groups over the Field of Two Elements

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On the maximality of the orthogonal groups in the symplectic groups in characteristic two

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Maximal subgroups of $GL_{2n}(K), SL_{2n}(K), PGL_{2n}(K)$ and $PSL_{2n}(K)$ associated with symplectic polarities

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Alternating groups as maximal subgroups of the special orthogonal groups over the field of two elements

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Automorphism sequences of integer unimodular groups

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Decomposition of equiaffinities into reflections

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Relations in classical groups

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Factorization of Affinities

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Q3873104

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Relations in the projective general linear group and in the affine subgroup

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Non-free groups generated by two parabolic matrices

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Q3934603

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Crystallographic groups and their mathematics

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Projective Representations of Minimum Degree of Group Extensions

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Complex linear groups of degree less than $2^{1/2}p-3$

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On finite complex linear groups of degree (q-1)/2

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Finite linear groups of degree less than p-2

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Complex linear groups of degree at most (q-1)/2

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On the Group of Integral Automorphs of a Positive Definite Quadratic Form

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Congruence Subgroups of the Picard Group

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A presentation of the symplectic and orthogonal groups

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On the $GE_n$ of a ring

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On the number of subgroups of given index in the modular group

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Q3899138

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Generators and Relations for the Special Linear Group Over a Division Ring

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A unipotent group associated with certain linear groups

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Free non-Abelian quotients of $SL_ 2$ over orders of imaginary quadratic numberfields

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A remark concerning unipotent matrix groups

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A geometric characterization of orthogonal groups for characteristic 2

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Isomorphism theory for orthogonal groups over arbitrary integral domains

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Unipotent elements and the spinor norms of Wall and Zassenhaus

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Category equivalences and linear groups over rings

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The existence of regular orbits for nilpotent groups

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Some Theorems of Hall-Higman Type for Small Primes

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Finite groups of matrices over division rings

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Multiplicative commutators in division rings. II

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On the order of linear groups of fixed finite exponent

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Nilpotency in classical groups over a field of characteristic 2

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Q4175433

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On finite multiplicative subgroups of simple algebras of degree 2

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Q3960971

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Normalizers of Parabolic Subgroups of Reflection Groups

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Polynomial Invariants of Finite Linear Groups of Degree Two

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Imprimitive linear groups generated by elements containing an eigenspace of codimension two

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Linear groups of degree nine with no elements of order seven

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Q3934684

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Linear Groups as Stabilizers of Sets

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Generators of a symplectic group over a local valuation domain

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Generators of on(v) over a quasi semi local semi hereditary domain

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Generators of spn(V) over a Quasi se-milocal semihereditary domain

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Generators of $U_n(V)$ over a quasi semilocal semihereditary domain

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Q3913589

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Generators of $Sp_ n($V) over a quasi semilocal semihereditary ring

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Simple coefficient extensions of symplectic groups

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Generators of Orthogonal Groups over Valuation Rings

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Structure of O(V) over full rings

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Q3964779

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Unitary groups over local rings

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Homomorphisms of unitary groups

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Abstract homomorphisms of algebraic groups: problems and bibliography

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On the geometry of unitary groups

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The automorphisms of the orthogonal groups Ωn(V), n5.

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A NOTE ON SUBGROUPS OF SL(2, C)

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Some remarks on nilpotent orbits

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Homology stability for linear groups

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Q3861572

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Q3909143

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Q4155073

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Permutation representations of the finite classical groups of small degree or rank

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Subgroups of Classical Groups Generated by Long Root Elements

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Linear groups containing a Singer cycle

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The Rank 3 Permutation Representations of the Finite Classical Groups

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Über einfache, lokal endliche Gruppen

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Some Maximal Subgroups of Certain Projective Unimodular Groups

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Maximal subgroups of the classical groups associated with non-isotropic subspaces of a vector space

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On some maximal subgroups of the classical groups

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Imprimitive Maximal Subgroups of the General Linear, Special Linear, Symplectic and General Symplectic Groups

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Maximal subgroups of the orthogonal group over a field of characteristic two

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Die Normalteiler der symplektischen Gruppen über beliebigen lokalen Ringen

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Explizite Präsentation gewisser Hilbertscher Modulgruppen durch Erzeugende und Relationen.

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The symplectic group over a ring with one in its stable range

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Lineare p-auflösbare Gruppen

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Theorem B of Hall-Higman revisited

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Normalteiler ganzzahliger Spingruppen.

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Erzeugung ganzzahliger orthogonaler Gruppen durch Spiegelungen

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The second degree cohomology of finite orthogonal groups. I

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Q4138849

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p-soluble linear groups with Sylow p-intersections of small rank

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The cusp amplitudes of the congruence subgroups of the classical modular group

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On unstable cohomology classes of SL n ( Z )

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The isomorphism theory of projective pseudo-orthogonal groups

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Euklidischer Algorithmus und die Gruppe $GL_2$

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On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group

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On permutation groups containing $O_{2n}$(2) as a subgroup

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Free quotients and the congruence kernel of $SL_ 2$.

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Numbers of conjugacy classes in some finite classical groups

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Products of Positive Reflections in the Orthogonal Group

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Maximal subgroups of infinite index in finitely generated linear groups

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A Note on Subgroups of GL(n, A ) which are Generated by Commutators

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A further note on subgroups of GL(n,A) which are generated by commutators

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Infinite General Linear Groups over Rings

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Automorphisms of GL n (R)

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Gl2of rings with many units

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Aut(GL2(R)) for rings with many units

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The orthogonal group over a full ring

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The orthogonal and the special orthogonal groups over a full ring

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Some groups generated by transvections

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Existentially closed linear groups

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On regular elliptic conjugacy classes of the Siegel modular group

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On orthogonal groups over the integers of a non-dyadic local field

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Unipotent Matrix Groups Over Division Rings

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Q3946713

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On Counting Types of Symmetries in Finite Unitary Reflection Groups

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Homology of SL(n,Z[1/p])

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On the subgroups of the group $PSL_4(2^m)$

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On some subgroups of PSL(4,q),q odd

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Normalizers of modular groups

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Das Relationenproblem für eine Klasse von Untergruppen orthogonaler Gruppen.

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On Bieberbach's Analysis of Discrete Euclidean Groups

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Solvable linear groups on vector spaces whose dimension is the product of two primes

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A polynomial bound for the orders of primitive solvable groups

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Normal congruence subgroups of the Hecke groups $G(2^{(1/2)})$ and $G(3^{(1/2)})$

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Q3894121

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Q3894122

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Q4148151

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The bravais group and the normalizer of a reducible finite subgroup of

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On Maximal Finite Irreducible Subgroups of GL(n, Z ): I. The Five and Seven Dimensional Cases

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On Maximal Finite Irreducible Subgroups of GL(n, Z ): II. The Six Dimensional Case

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On Maximal Finite Irreducible Subgroups of GL(n, Z ): III. The Nine Dimensional Case

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On Maximal Finite Irreducible Subgroups of GL(n, Z ): IV. Remarks on Even Dimensions with Applications to n = 8

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On maximal finite irreducible subgroups of 𝐺𝐿(𝑛,𝑍). V. The eight-dimensional case and a complete description of dimensions less than ten

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Q3937574

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An analogue of Maschke's theorem for certain representations of A6 over GF(2)

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Le théorème fondamental des invariants pour les groupes finis

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Subgroups of the unimodular group defined by a congruence

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On the finite imprimitive unitary reflection groups

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Zentrale Erweiterungen der speziellen linearen Gruppe eines Schiefkörpers.

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Die Kommutatorfaktorgruppe der Normeinsgruppe einer p-adischen Divisionsalgebra

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On $K_2$ of finite dimensional division algebras over arithmetical fields

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Q3950736

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Q3957140

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Subgroups of SL(2, R) freely generated by three parabolic elements

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Subgroups of finite groups of Lie type

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On the subgroup structure of classical groups

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Le problème des groupes de congruence pour $SL_2$

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Canonical reducible cubic forms in $n\;(\geq 3)$ variables and their infinite orthogonal groups

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Linear representations of certain amalgamated products

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On the structure of the Steinberg group st(Lambda)

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A Presentation for a Group of Integer Matrices

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On the Homology of the General Linear Groups Over Z/4

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Four-dimensional symplectic groups

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The cohomology of $SL_3(Z)$

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Q3858463

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Relative invariants of finite groups generated by pseudoreflections

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Invariants of finite groups and their applications to combinatorics

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Q4175440

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Q3050631

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The Schur multipliers of Sp$_6(Z)$, Spin$_8(Z)$, Spin$_7(Z)$ and F$_4(Z)$

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Generators, relations and coverings of algebraic groups. II

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Certain embeddings among finite groups of Lie type

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Subgroups of infinite index in the modular group

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Groups of the second kind within the modular group

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Unitäre Gruppen über beliebigen lokalen Ringen

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The symplectic group and determinants

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The fundamental group of the general linear group

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The second Lie algebra cohomology group and Weyl modules

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Q3913503

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On parabolic subgroups of Chevalley groups over local rings

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Representations of certain verbal wreath products by matrices

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Endliche Spiegelungsgruppen, die als Weylgruppen auftreten

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Quaternions over $Q(\sqrt5)$, Leech's lattice and the sporadic group of Hall-Janko

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Subgroups of SL2ℤ generated by elementary matrices

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On full subgroups in the sense of O'Meara

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Q3933170

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Transitivitaetsfragen bei linearen Gruppen

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The general linear group of polynomial rings over regular rings

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Sur la théorie classique des invariants

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Q4149879

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Q3952287

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Collineation groups generated by homologies of order greater than 2

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Q4185037

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The subgroups of $PSL(5,2^a)$

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Determination of the finite primitive reflection groups over an arbitrary field of characteristic not 2. I

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Linear groups of degree n containing an involution with two eigenvalues - 1. II

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Connections between finite linear groups and linear algebra

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Conjugacy classes in projective and special linear groups

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Automorphisms of GL n (R)

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Q4173563

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Nilpotence in Groups of Semi-Linear Maps

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Hypercentral Unipotent Subgroups of Linear Groups

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On finitely generated soluble linear groups

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The Rank of a Linear p -Group; An Apology

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Wielandt's subnormality criterion and linear groups

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Groups whose irreducible representations have finite degree

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Groups whose irreducible representations have finite degree: III

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Q3912660

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Abstract monomorphisms between big subgroups of some groups of type $B_2$ in characteristic 2

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Q3947833

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On the Hall-Higman and Shult theorems

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full work available at URL

https://doi.org/10.1007/bf02106807

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OpenAlex ID

W3190212900

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Sitelinks

Mathematics(1 entry)

mardi Publication:5902851