Group algebras of abelian groups
Group Algebras of Finite Representation Type.
Group algebras of polynomial growth.
Group algebras with centrally metabelian unit groups.
Given a field K of characteristic p > 2 and a finite group G, necessary and sufficient conditions for the unit group U(KG) of the group algebra KG to be centrally metabelian are obtained. It is observed that U(KG) is centrally metabelian if and only if KG is Lie centrally metabelian.
Group extensions and automorphism group rings.
Group Extensions and Splitting Modules.
Group representations and integrality.
Group representations without groups.
Group rings and irreducible representations of space groups.
Group rings, Hecke orders, quasi-hereditary orders, cellular orders and deformations.
Group Rings of Circle and Unit Groups.
Group Rings of Finite Representation Type.
Group Rings of Hypercyclic Groups.
Group Rings Whose Units Form an FC-Group.
Group Rings Whose Units Form an FC-Group.
Group rings with FC-nilpotent unit groups.
Let U(RG) be the unit group of the group ring RG. Groups G such that U(RG) is FC-nilpotent are determined, where R is the ring of integers Z or a field K of characteristic zero.
Group Rings with Units Torsion Over the Center.
Groups All of Whose Subgroups are M-Groups.
Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL for
Let be a finite group and write for the degree set of the complex irreducible characters of . The group is said to satisfy the two-prime hypothesis if for any distinct degrees , the total number of (not necessarily different) primes of the greatest common divisor is at most . We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL for .
...-Groups that are M-Groups.