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Geometry of 1-tori in $\mathrm {GL}_n$ - MaRDI portal

Geometry of 1-tori in $\mathrm {GL}_n$ (Q3053927)

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Language	Label	Description	Also known as
English	Geometry of 1-tori in $\mathrm {GL}_n$	scientific article

Statements

scholarly article

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Geometry of 1-tori in $\mathrm {GL}_n$ (English)

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St. Petersburg Mathematical Journal

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publication date

5 November 2010

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zbMATH Keywords

general linear groups

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unipotent root subgroups

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numbers of orbits

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pseudoreflections

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one-dimensional tori

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diagonal subgroups

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orbitals

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intermediate subgroups

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Nikolai A. Vavilov

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MaRDI profile type

MaRDI publication profile

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Linear groups generated by two long root subgroups

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On subgroup of the special linear group of degree 2 over an infinite field

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Linear groups containing a root subgroup

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On subgroups of the general linear group over the skew field of quaternions containing the special unitary group

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Linear groups generated by one-parameter groups of one-dimensional transformations

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On subgroups of the unitary group over a semilocal ring

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The intersection of two Bruhat cells.

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Bruhat decomposition for long root tori in Chevalley groups

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On overdiagonal subgroups of the hyperbolic unitary group for a skew field.

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Overdiagonal subgroups of the hyperbolic unitary group for a good form ring over a skew field.

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Linear groups generated by two-dimensional elements of order r\(\geq 5\)

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Pairs of short root subgroups in Chevalley groups

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The arrangement of long and short root subgroups in a Chevalley group of type \(G_2\).

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Pairs of short root subgroups in the Chevalley group of type \(G_2\).

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Odd unitary groups.

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Sur certains groupes simples

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Involutions in Chevalley groups over fields of even order

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Structure of Hyperbolic Unitary Groups I: Elementary Subgroups

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Some Completely Reducible Linear Groups over a Quaternion Division Ring Containing a Root Subgroup

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Irreducible Linear Groups of Degree 3 Over a Quaternion Division Ring Containing a Root Subgroup

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Irreducible linear groups of degree four over a quaternion division algebra that contain a subgroup \(\text{diag}(T_3(K,\Phi_0),1)\).

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Linear groups generated by a pair of quadratic action subgroups

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Extensions of Chevalley groups

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Orbits Under Symplectic Transvections I

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Some groups generated by transvection subgroups

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Finite complex reflection groups

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Finite quaternionic reflection groups

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Linear Groups Generated by Reflection Tori

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Subgroups of the group \(E_6(q)\) which are generated by root subgroups

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The geometry of root subgroups in exceptional groups. II

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Subgroups of exceptional groups of Lie type generated by long root elements. II. Characteristic two

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Finite groups generated by unitary reflections

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A characterization of \(SL_ 2(k)\) by its quadratic action on the natural module

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Symplectic geometries, transvection groups, and modules

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Linear transvection groups and embedded polar spaces

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SPECIAL LINEAR GROUPS GENERATED BY TRANSVECTIONS AND EMBEDDED PROJECTIVE SPACES

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(2,3)-Generation of sl(n,q). II. cases n ≥ 8

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Maximality of the monomial group

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On the lattice of subgroups of chevalley groups containing a split maximal torus

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Linear groups containing an element with an eigenspace of codimension two

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Linear groups of degree<i>n</i>containing an element with exactly n–2 equal eigenvalues

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Linear groups containing an involution with two eigenvalues -1

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On the geometry of unitary groups

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Subgroups of Classical Groups Generated by Long Root Elements

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Subgroups of the special linear group containing the diagonal subgroup

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The maximality of monomial subgroups of linear groups over division rings

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Irreducible subgroups of SL(n,K) generated by root subgroups

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Subgroups generated by root elements in groups of Lie type

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Some groups generated by transvections

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Overgroups of unitary groups.

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Subgroups of finite groups of Lie type

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Finite Unitary Reflection Groups

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Some subgroups of \(\Omega (V)\) generated by groups of root type 1

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Some subgroups of \(\Omega\)(V) generated by groups of root type

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Irreducible subgroups of orthogonal groups generated by groups of root type 1

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Another look at Thompson's quadratic pairs

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Subgroups of classical groups generated by transvections or Siegel transvections. II: Embeddings in orthogonal groups

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Subgroups isomorphic to \(G_2(L)\) in orthogonal groups

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Subgroups of the Chevalley groups of type <i>F<sub>4</sub> </i> arising from a polar space

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Groups generated by k-transvections

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Groups generated by \(k\)-root subgroups

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Moufang planes and the groups E K 6and SL 2 (K), Ka Cayley division algebra

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Subgroups generated by root-elements of groups generated by \(k\)-root subgroups

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Abstract root subgroups and quadratic action. With an Appendix by A. E. Zalesskii

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A conjugacy theorem for subgroups of $GL_n$ containing the group of diagonal matrices

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Unipotent elements in subgroups which contain a split maximal torus

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Groups generated by elations

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Collineation groups generated by homologies of order greater than 2

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Determination of the finite primitive reflection groups over an arbitrary field of characteristic not two. II

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

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Abstract monomorphisms between big subgroups of some groups of type \(B_2\) in characteristic 2

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Monomorphisms between subgroups of groups of type \(G_ 2\).

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Abstract isomorphisms of simple algebraic groups split by quadratic extensions

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full work available at URL

https://doi.org/10.1090/s1061-0022-08-01004-2

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Identifiers

zbMATH Open document ID

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10.1090/S1061-0022-08-01004-2

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3053927

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