Integral group rings: Groups of units and classical K-theory

DOI10.1007/BF01099283zbMath0732.16020OpenAlexW2017072007MaRDI QIDQ809166

Vyacheslav A. Artamonov, Adalbert Bovdi

Publication date: 1991

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01099283

zbMATH Keywords

surveyintegral group ringsmultiplicative groupselements of finite orderclassical K-theoryCongruence-subgroupsFree subgroupsnormalized multiplictive groupProjective modulesunitary subgroup

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Grothendieck groups, (K)-theory, etc. (16E20) 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

Torsion units for a Ree group, Tits group and a Steinberg triality group. ⋮ Unnamed Item ⋮ Traces of Torsion Units ⋮ Quotients of Passman fours group and non-units of their group algebras ⋮ Partial augmentations power property: a Zassenhaus conjecture related problem ⋮ Units in orders and integral semigroup rings. ⋮ On partial augmentations of elements in integral group rings ⋮ Torsion units for some almost simple groups ⋮ Torsion units for some projected special linear groups ⋮ Integral group ring of the Mathieu simple group \(M_{12}\). ⋮ Finite simple groups with short Galois orbits on conjugacy classes

Cites Work

• \(SK_ 1\) of finite group rings. V
• Torsion units of integral group rings of metacyclic groups
• Certain conjugacy classes of units in integral group rings of metacyclic groups
• Groups which are normal in the unit groups of their group rings
• Periodic resolutions for finite groups
• Torsion units in integral group rings of metacyclic groups
• Units in Whitehead groups of finite groups
• Structure of group bases of a group ring
• On a conjecture of Zassenhaus on torsion units in integral group rings
• Some remarks on the unit groups of integral group rings
• \(SK_1\) of finite Abelian groups. I
• The group of normalized units of a group ring
• Units in group rings: Splittings and the isomorphism problem
• On the automorphism group of the p-adic group ring of a metacyclic p- group. II
• Torsion units in integral group rings of some metabelian groups
• Units in regular elementary Abelian group rings
• \(SK_1\) of finite abelian groups. II
• Torsion units in integral group rings of some metabelian groups. II
• Units in \({\mathbb{Z}}[Q_ p\)]
• A Mayer-Vietoris sequence for Picard groups, with applications to integral group rings of dihedral and quaternion groups
• Unitary subgroup of the multiplicative group of the integral group ring of a cyclic group
• Homotopy representation groups and Swan subgroups
• 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
• Torsion free cancellation over orders
• Groups, trees and projective modules
• \(SK_1\) for finite groups rings. I
• Integral representations. Topics in integral representation theory by I. Reiner. Integral representations and presentations of finite groups by K. W. Roggenkamp
• Surjective stability of units and simple homotopy type
• On the units of integral group rings
• A characterization of units in \(\mathbb{Z} [A_4\)]
• Units in integral group rings
• Einheiten in Z(D//2m)
• Integral group rings with residually nilpotent unit groups
• Projective modules over group-algebras of torsion-free groups
• Units of integral group rings of metabelian groups
• On the isomorphism problem for integral group-rings of circle-groups
• Group algebras over finitely generated rings
• Nontrivial lower bounds for class groups of integral group rings
• \(K_0\) and noetherian group rings
• On the automorphism group of an integral group ring. I
• Euler characteristics and characters of discrete groups
• Locally free classgroups of groups of prime power order
• The locally free classgroup of the symmetric group
• On the isomorphism problem for integral group rings
• On the projective class group of arithmetic groups
• Units in metabelian group rings: Non-splitting examples for normalized units
• The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
• Idempotent ideals in integral group rings
• The Grothendieck ring of a finite group
• Whitehead Groups of Some Hyperelementary Groups
• The Group of Units of the Integral Group Ring ZS₃
• Isomorphism of integral group rings of abelian by nilpotent class two groups
• Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings
• Free Subgroups of Units in Group Rings
• The Whitehead Group of Poly-(Finite or Cyclic) Groups
• Conjugacy classes of torsion units of the integral group ring of d_p
• Class groups of cyclic p ‐groups
• Normal and subnormal subgroups in the group of units of group rings
• Group rings with solvable unit groups
• On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings. II
• Idempotents and zero divisors in group rings
• On the torsion units op integral dihedral group rings
• Induction theorems for infinite groups
• A characterization of units in zs₄
• Units in Integral Group Rings of Some Metacyclic Groups
• On the Stable Range of Right Noetherian Rings
• A note on u.p. groups
• K -Theory and Stable Structure of Some Noetherian Group Rings
• Groups rings: an annotated questionnaire
• Group Rings Whose Torsion Units Form a Subgroup
• Nonfree Projective Modules for Integral Group Rings
• Free Subgroups in the Unit Groups of Integral Group Rings
• UNITS IN INTEGRAL METABELIAN GROUPRINGS I, JACKSON'S UNIT THEOREM REVISITED
• Group rings whose torsion units form a subgroup II
• On commutative group algebras
• Integral Group Rings of Some p-Groups
• SK ₁ for Finite Group Rings: IV
• A Note on Nonfinitely Generated Projective Zπ-Modules
• Projective modules over binary polyhedral groups.
• Isomorphe Gruppenringe lokal endlicher Gruppen.
• Integral Group Rings with Nilpotent Unit Groups
• Projective class groups of symmetric and alternating groups
• The Homotopy Type of a Two-Dimensional Complex
• On the Trace of an Idempotent in a Group Ring
• Integral group rings with nilpotent unit groups
• ON THE STRUCTURE OF THE SPECIAL LINEAR GROUP OVER POLYNOMIAL RINGS
• The group of units of the integral group ring ℤD 4 *
• Whitehead groups of finite groups
• On the Conjugacy Classes in an Integral Group Ring
• Non-Free Projective Modules for Torsion-Free Groups
• Projective Modules over Laurent Polynomial Rings
• Ranks of projective modules of group rings
• On the group ring of a finite abelian group
• THE GROUPS OF UNITS OF THE INTEGRAL GROUP RINGS OF FINITE METABELIAN AND FINITE NILPOTENT GROUPS
• "Problems in the Theory of Rings" Revisited
• On Class Sums in p-Adic Group Rings
• Class groups for integral representations of metacyclic groups
• Isomorphisms of p-adic group rings
• Units of group rings
• Group rings whose units form an FC-group
• Group rings whose units form an FC-group
• Note on the integral group ring problem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Integral group rings: Groups of units and classical K-theory