A note on group rings with trivial units

Document Type

Article

Publication Date

4-1-2022

Abstract

Let R be a ring with identity of characteristic two and G a nontrivial torsion group. We show that if the units in the group ring RG are all trivial, then G must be cyclic of order two or three. We also consider the case where R is a commutative ring with identity of odd prime characteristic and G is a nontrivial locally finite group. We show that in this case, if the units in RG are all trivial, then G must be cyclic of order two. These results improve on a result of Herman et al. 'Trivial units for group rings with G-adapted coefficient rings', Canad. Math. Bull. 48(1) (2005), 80-89].

Keywords

Group ring, Unit, Torsion group, Locally finite group

Publication Title

Bulletin of The Australian Mathematical Society

Divisions

Science

Funders

None

Volume

105

Issue

2

Publisher

Cambridge Univ Press

Publisher Location

EDINBURGH BLDG, SHAFTESBURY RD, CB2 8RU CAMBRIDGE, ENGLAND

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