Describing units of integral group rings up to commensurability

2014/01/30 by Florian Eisele, Eisele, Florian, Ann Kiefer +3 · 1 citation
Mathematics · #16S34 #16U60 #20C05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:16S34 #msc:16U60 #msc:20C05

paper · pdf · doi:10.48550/arxiv.1401.7854

Revised version. Accepted for publication in J. Pure and Appl. Algebra

arxiv created 2014/09/17 · arxiv updated 2014/09/18

Abstract

We restrict the type of 2 × 2-matrices which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units of the integral group ring \mathbb Z G for all finite groups G that do not have a non-commutative Frobenius complement as a quotient.

Cited by

• A unit theorem for products of groups with several ends and Applications

Related

• Structure of group rings and the group of units of integral group rings: an invitation
• Groups of units of integral group rings commensurable with direct products of free-by-free groups
• Central units of integral group rings*
• Finite groups in integral group rings
• Central units of integral group rings