Accessible Requires Authentication Published by De Gruyter September 13, 2006

Commutativity of symmetric elements in group rings

Osnel Broche Cristo
From the journal

Abstract

Let R be a commutative ring with unity and let G be a group. The group ring RG has a natural involution that maps each element of G to its inverse. We denote by RG+ the set of symmetric elements under this involution. We study necessary and suffient conditions for RG+ to be commutative or, equivalently, for RG+ to be a subring of RG. We also determine all torsion groups G such that the set of symmetric units of RG is a subgroup, when char(R) is an odd prime number.


(Communicated by C. W. Parker)


Received: 2004-03-31
Revised: 2005-08-30
Published Online: 2006-09-13
Published in Print: 2006-09-01

© Walter de Gruyter