Vol. 47, No. 1, 1973

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On the semisimplicity of group rings of linear groups

Donald Steven Passman

Vol. 47 (1973), No. 1, 221–228

In this paper we study the semisimplicity problem for group rings of linear groups. We prove the linear group analog of a result which constitutes part of the solution of the semisimplicity problem for solvable groups. Since all of the necessary group ring lemmas have appeared elsewhere, the work here is strictly group theoretic. We consider the possibility of a linear group being covered by a finite union of root sets of centralizer subgroups.

Mathematical Subject Classification 2000
Primary: 20C05
Received: 23 March 1972
Published: 1 July 1973
Donald Steven Passman