Linear identities in group rings. I

Donald Steven Passman

Vol. 36 (1971), No. 2, 457–483

DOI: 10.2140/pjm.1971.36.457

Abstract

Let K[G] denote the group ring of a (not necessarily finite) group G and suppose that this ring satisfies a nontrivial polynomial identity of degree n. If Δ denotes the finite conjugate subgroup of G, then we show that [G : Δ] ≦ n!. Furthermore, if K[G] is semiprime, then G has an abelian subgroup of finite bounded index.

Mathematical Subject Classification

Primary: 20.80

Milestones

Received: 25 May 1970

Published: 1 February 1971