A commutative version of the group ring

Abstract

We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an alternative proof of a result about the normal generation of the free product of two cyclic groups.Comment: 31 pages, preprint. Reason for revision: additions to content; in particular rewritten Section 5 and new Section 6 adde