scientific article; zbMATH DE number 2156375
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Publication:4668864
zbMath1078.16022MaRDI QIDQ4668864
Publication date: 15 April 2005
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Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Units, groups of units (associative rings and algebras) (16U60) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)
Related Items (4)
The isomorphism problem for group algebras: a criterion ⋮ Abelianization and fixed point properties of units in integral group rings ⋮ Rational group algebras of finite groups: from idempotents to units of integral group rings. ⋮ From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups
Cites Work
- Brauer induction for \(G_ 0\) of certain infinite groups
- Torsion units of integral group rings of metacyclic groups
- The seventh and eighth Lie dimension subgroups
- Groups which are normal in the unit groups of their group rings
- On universal derivations
- Finite Abelian groups with isomorphic group algebras
- Groups with representations of bounded degree. II
- Arithmetic subgroups of algebraic groups
- Units in the modular group algebra of a finite Abelian p-group
- Torsion units in integral group rings of metacyclic groups
- Integral group rings: Groups of units and classical K-theory
- On the Lie ideals of a ring
- On a conjecture of Zassenhaus on torsion units in integral group rings
- Cyclotomic units and the unit group of an elementary Abelian group ring
- On Lie nilpotent group rings
- Some remarks on the unit groups of integral group rings
- The group of normalized units of a group ring
- Units in group rings: Splittings and the isomorphism problem
- Some isomorphism invariants of integral group rings
- On the classnumber of some group rings
- Torsion units in integral group rings of some metabelian groups
- Units in regular elementary Abelian group rings
- Free subgroups in the group of units of group rings. II
- Torsion units in integral group rings of some metabelian groups. II
- Units in \({\mathbb{Z}}[Q_ p\)]
- Group automorphisms inducing the identity map on cohomology
- Units and class-groups in integral elementary Abelian group rings
- The modular group algebra of a central-elementary-by-abelian p-group
- A theorem on units of integral group rings
- Identifications in a free group
- Isomorphism of group rings of infinite nilpotent groups
- Rigidity of \(p\)-adic \(p\)-torsion
- Moody's induction theorem
- Logarithms and units in p-adic Abelian group rings
- Units in regular Abelian p-group rings
- Elements of finite order in \(V(ZA_ 4)\)
- Zassenhaus conjecture for \(A_5\)
- Nil ideals in group rings
- A characterization of units in \(\mathbb{Z} [A_4\)]
- Bounding the number of generators of a polycyclic group
- Group rings with units torsion over the centre
- The zero divisor conjecture for some solvable groups
- Finite normalizing extensions of rings
- Units in integral group rings
- Einheiten in Z(D//2m)
- Integral group rings with residually nilpotent unit groups
- Units of integral group rings of metabelian groups
- The Lie dimension subgroup conjecture
- Construction of units in group rings of monomial and symmetric groups
- On the automorphism group of the integral group ring of \(S_ k \text{wr} S_ n\)
- Semigroup identities on units of group algebras
- Residually Lie nilpotent group rings
- Constructing units in commutative group rings
- Local units and circular index in abelian \(p\)-group rings
- Idempotent elements and ideals in group rings and the intersection theorem
- Advances in group rings
- Nilpotent elements in group rings
- A note on idempotent ideals in group rings
- Certain algebraic elements in group rings
- PI-algebras. An introduction
- The fourth dimension subgroups and polynomial maps
- \(K_0\) and noetherian group rings
- Group rings without nontrivial idempotents
- On the automorphism group of an integral group ring. I
- Euler characteristics and characters of discrete groups
- The residual nilpotency of the augmentation ideal and the residual nilpotency of some classes of groups
- On the automorphism group of an integral group ring. II
- Dimension and lower central subgroups
- New light on Frobenius' creation of the theory of group characters
- Group rings and their augmentation ideals
- Symmetric units and group identities
- Gauss units in integral group rings
- Free products of units in algebras. I: Quaternion algebras
- Finite groups of the Lie type of small rank
- Generators of large subgroups of the unit group of integral group rings
- Automorphisms of the integral group ring of the wreath product of a \(p\)- group with \(S_ n\), the case \(n=2\)
- Torsion units in infinite group rings
- Idempotents in matrix group rings
- Group identities on units of rings
- Group theoretic and group ring theoretic determination of certain Sylow and Hall subgroups and the resolution of a question of R. Brauer
- Nonmatrix varieties and nil-generated algebras whose units satisfy a group identity
- Products of free groups in the unit group of integral group rings. II
- Automorphisms of generic Iwahori-Hecke algebras and integral group rings of finite Coxeter groups
- On the semisimplicity of group rings of some locally finite groups
- Représentation de \(-1\) comme somme de carrés dans un corps cyclotomique quelconque
- Torsion matrices over commutative integral group rings
- An introduction to group rings
- Units of group rings of solvable and Frobenius groups over large rings of cyclotomic integers
- The determination of abelian Hall subgroups by a conjugacy class structure
- Automorphisms of the integral group ring of the wreath product of a \(p\)- group with \(S_ n\)
- Tensor products and a conjecture of Zassenhaus
- Torsion-free group without unique product property
- Isomorphism of group rings
- Units in metabelian group rings: Non-splitting examples for normalized units
- Nichtkommutative Algebra
- Group rings of circle and unit groups
- Integral group rings of solvable finite groups have no idempotent ideals
- Group rings of polycyclic groups
- Hirsch induction and torsion units in group rings
- Generators of large subgroups of units of integral group rings of nilpotent groups
- Degree 1 and 2 representations of nilpotent groups and applications to units of group rings
- Autoequivalences of blocks and a conjecture of Zassenhaus
- Large subgroups in the unit groups of arithmetic orders
- On the isomorphism problem for infinite group rings
- Units of classical orders: A survey
- Products of free groups in the unit group of integral group rings
- Finite matrix groups over nilpotent group rings
- Zassenhaus conjecture and infinite nilpotent groups
- Group identities on units of group algebras
- A new radical for group rings?
- The group algebras of groups of order \(p^ 4\) over a modular field
- On the groups with the same table of characters as alternating groups
- Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
- Solvable groups with isomorphic group algebras
- The Jacobson radicals of the group algebras of a group and of certain normal subgroups
- On the free product of associative rings. III
- Dimension subgroups
- On the isomorphism of group algebras
- The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
- Some applications of subnormality in groups in the study of group algebras
- Isomorphic groups and group rings
- Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
- Deux groupes finis distincts ayant la même algèbre de groupe sur tout corps
- Cohomological topics in group theory.
- Isomorphism of p-adic group rings
- The origin of the theory of group characters
- Group algebras
- Fixed point free actions on p-groups
- A note on the adjoint group of a ring
- Integral group rings of finite groups
- Group rings satisfying a polynomial identity
- On the units of orders
- The dimension subgroup problem
- Dimension subgroups over arbitrary coefficient rings
- Group rings satisfying a polynomial identity. II
- Isomorphism of modular group algebras
- Primitive group rings
- Free subgroups in linear groups
- Idempotent ideals in integral group rings
- On the semisimplicity of group rings of linear groups. II
- On the semisimplicity of group rings of linear groups
- Hypercomplex numbers, Lie groups, and the creation of group representation theory
- Idempotent ideals in integral group ring. II
- On the fourth integer dimension subgroup
- Constructible units in Abelian p-group rings
- Ein Verfahren, jeder endlichen \(p\)-Gruppe einen Lie-Ring mit der Charakteristik \(p\) zuzuordnen
- Discontinuous groups
- Hypercentral units in integral group rings
- Applications of a New K-Theoretic Theorem to Soluble Group Rings
- Constructing free subgroups of integral group ring units
- Finite Subgroups in Integral Group Rings
- Free torsion-free normal complements in integral group rings
- Central height of the unit group of an integral group ring
- Lie nilpotence of group rings
- Automorphisms of the integral group ring of the hyperoctahedral group
- Describing units of integral group rings of some 2-groups
- Construction of Units in Integral Group Rings of Finite Nilpotent Groups
- The Group of Units of the Integral Group Ring ZS3
- Radicals Of Polynomial Rings
- Residual Properties of Infinite Soluble Groups
- The Structure of Prime Rings Under Ascending Chain Conditions
- Semi-Prime Rings with Maximum Condition
- Group algebras with radicals of square zero
- Isomorphism of integral group rings of abelian by nilpotent class two groups
- Automorphisms of the integral group rings of some wreath products
- Restricted lie dimension subgroups
- Zassenhaus conjecture for S5
- Free Subgroups of Units in Group Rings
- Conjugacy classes of torsion units of the integral group ring of dp
- Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
- Integral Group Rings Without Proper Units
- K 0 of Skew Group Rings and Simple Noetherian Rings without Idempotents
- Group rings with solvable unit groups
- UNITS AND ISOMORPHISM IN GROUP RINGS
- Functors on Finite Vector Spaces and Units in Abelian Group Rings
- A note on central idempotents in group rings
- On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings. II
- Induction theorems for infinite groups
- A characterization of units in zs4
- Units in Integral Group Rings of Some Metacyclic Groups
- Subnormal Subgroups in U( Z G)
- A Simple Example of a Torsion-Free, Non Unique Product Group
- The Isomorphism Question for Modular Group Algebras of Metacyclic p-Groups
- Bass conjecture and the group trace property
- Subnormal subgroups of group ring units
- Free products of abelian groups in the unit group of integral group rings
- Polynomial Ideals in Group Rings
- Congruence subgroups in group rings*
- On the Structure of Integral Group Rings of Sporadic Groups
- Bicyclic Units in some Integral Group Rings
- $KD_\infty $ is a CS-algebra
- Finite groups of matrices over group rings
- Central Idempotents and Units in Rational Group Algebras of Alternating Groups
- A Note on the Unit Group of ZS 3
- Integral group rings whose group of units is solvable an elementary proof
- A Remark on the Units of Finite Order in The Group Ring of a Finite Group
- Conjugates of units in integral group rings
- Symmetric units in modular group algebras
- Central units of integral group rings of nilpotent groups
- The modular group algebra problem for metacyclic 𝑝-groups
- Central units of integral group rings*
- Torsion matrices over abelian group rings
- The lien-engel property in group rings
- Groups related to fox subgroups
- A structure theorem for the unit group of the integral group ring of some finite groups
- Groups with Representations of Bounded Degree
- Finite Groups With Isomorphic Group Algebras
- On the Structure of Group Algebras, I
- On the Modular Group Ring of a p-Group
- A COUNTEREXAMPLE IN NOETHERIAN RINGS
- Shorter Notes: Idempotents in Group Rings
- On the group ring of a finite abelian group
- Group Algebras with Nilpotent Unit Groups
- On Commutative and Central Conditions on the Jacobson Radical of the Group Algebra of a Group
- On the Isomorphism of Integral Group Rings. I
- Commutative Group Algebras
- THE GROUPS OF UNITS OF THE INTEGRAL GROUP RINGS OF FINITE METABELIAN AND FINITE NILPOTENT GROUPS
- On the Isomorphism of Integral Group Rings. II
- The Residual Nilpotence of Wreath Products
- On Group Rings
- On Noetherian Prime Rings
- Units in Modular Group Rings
- "Problems in the Theory of Rings" Revisited
- Localization in Group Rings
- Central Idempotents in Group Rings
- On Perfect Group Rings
- Quotient Rings of Group Rings
- On Class Sums in p-Adic Group Rings
- The radical of the group algebra of a sub-group, of a polycyclic group and of a restricted SN-group
- Idempotents in Group Rings
- Ideals in the Modular Group Ring of a p-Group
- On the Solvability of Unit Groups of Group Algebras
- An elementary note on group-rings.
- A Short Proof of a Theorem of Jennings
- Local Rings and Normalizing Sets of Elements
- Idempotents in Noetherian Group Rings
- On the Ring of Quotients of a Group Ring
- Group Rings Satisfying a Polynomial Identity. III
- On the Dimension of Group Rings
- A Note on Zero Divisors in Group-Rings
- Some Results on Semi-Perfect Group Rings
- A Note on Group Rings of Certain Torsion-Free Groups
- On the units of a modular group ring
- On the units of a modular group ring II
- N-Series and Filtrations of the Augmentation Ideal
- The zero divisor question for supersolvable groups
- On the Structure of Q2(G) for Finitely Generated Groups
- A Lie Property in Group Rings
- The Modular Group Algebras of P-Groups of Maximal Class
- An Induction Theorem for Units of p-Adic Group Rings
- Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups
- A note on u.p. groups
- Groups rings: an annotated questionnaire
- Zero Divisors and Idempotents in Group Rings
- The structure of modules over polycyclic groups
- Free Subgroups in the Unit Groups of Integral Group Rings
- Fc-elements in a group ring
- A Problem of R. H. Fox
- Group Rings with Units of Bounded Exponent over the Center
- Lie algebra associated with linear group
- Integral Group Rings of Some p-Groups
- Torsion units in integral group rings.
- Construction of a counterexample to a conjecture of zassenhaus
- Torsion units in matrix group rings
- Jordan decomposition and hypercentral units in integral group rings
- THE STRUCTURE OF CLASSICAL ARITHMETIC GROUPS OF RANK GREATER THAN ONE
- What is a Group Ring?
- Integral Group Rings with Nilpotent Unit Groups
- Lie dimension subgroups
- A Note on Hypercentral Group Rings
- Isomorphic Group Rings
- On Zero Divisors in Group Rings
- Group Rings with Solvable n-Engel Unit Groups
- On the Trace of an Idempotent in a Group Ring
- Automorphisms of the Integral Group Ring of S n
- Integral group rings with nilpotent unit groups
- ON THE GROUPSL2OVER DEDEKIND RINGS OF ARITHMETIC TYPE
- The fourth dimension subgroups and polynomial maps, II
- Periodic Modules over Modular Group Algebras
- Observations on group rings
- The group of units of the integral group ring ℤD 4 *
- When is the unit group of a dedekind order solvable?
- Shorter Notes: Group Rings whose Units Form a Nilpotent or FC Group
- Residual solvability of unit groups of local group rings
- The elements of finite order in the group of units of group rings of free products of groups
- Construction of units in integral group rings of finite nilpotent groups
- Integral Group Rings with Trivial Central Units
- Algebraic Elements in Group Rings
- Units in Group Rings of Free Products of Prime Cyclic Groups
- The Hypercentre and the n-Centre of the Unit Group of an Integral Group Ring
- Finitely generated group ring units
- Group algebras with units satisfying a group identity
- Group algebras with units satisfying a group identity II
- Units in integral group rings over Solomon fields
- Group rings whose symmetric elements are Lie nilpotent
- On the normalizer property for integral group rings
- Units of group rings of groups of order 16
- Torsion Units in Integral Group Rings
- Bicyclic and Bass Cyclic Units in Group Rings
- Torsion units in integral group rings of solvable groups
- Units of Integral Group Rings of Some Metacyclic Groups
- Free Normal Complements and the Unit Group of Integral Group Rings
- HIGMAN’S CENTRAL UNIT THEORY, UNITS OF INTEGRAL GROUP RINGS OF FINITE CYCLIC GROUPS AND FIBONACCI NUMBERS
- Units of integral group rings of hamiltonian groups*
- Group algebras whose units satisfy a group identity
- Group algebras whose units satisfy a group identity. II
- Handling integralp-Group rings
- Integral group rings of frobenius groups and the conjectures of H.J. Zassenhaus
- The modular fox subgroups
- Construction of free subgroups in the group of units of modular group algebras
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- Lie Solvable Group Rings
- Central units of the integral group ring $\mathbb {Z}A_5$
- On Dimension Subgroups
- On the Group Ring
- On Groups of Order p3
- Determining Units in Some Integral Group Rings
- The Dimension Subgroup Conjecture
- The Units of Group-Rings
- The Structure of the Group Ring of a p-Group Over a Modular Field
- On rings whose associated Lie rings are nilpotent
- On Ordered Division Rings
- Groups with Representations of Bounded Degree
- Abelian Group Algebras of Finite Order
- Groups with Finite Classes of Conjugate Elements (In Memoriam Issai Schur)
- Generalization of a Theorem of Magnus
- The Identities of PI-Rings
- Sur les groupes nilpotents et les anneaux de Lie
- Finiteness Conditions for Soluble Groups
- The Group Ring Of a Class Of Infinite Nilpotent Groups
- Isomorphisms of p-adic group rings
- Idempotents in group rings
- Group rings
- Units of group rings
- Group rings whose units form an FC-group
- Artinian quotient rings of group rings
- Units of group rings
- Linear identities in group rings. I
- Note on the integral group ring problem
- A counterexample to the isomorphism problem for integral group rings
- Free unit groups in group algebras
- Group rings whose units form an FC-group
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