The Sufficient and Necessary Conditions on Group G So that U is Locally Finite and Finitely Generated

Abstract

Let G be a group and A be a ring . let U be the units group in the group ring A[G]. Many recent studies in algebra deal with the structure of the group U knowing the structure of the group G and vice versa. In this paper we tried to prove the following problems . 1. What are the necessary and sufficient conditions on G so that U is locally finite? 2. What are the necessary and sufficient conditions on G so that U is finitely generated