Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings

Abstract

Abstract Let KG be the group ring of the group G over the field K and U ( KG ) its unit group. When G is finite we derive conditions which imply that every noncentral subnormal subgroup of U ( KG ) contains a free group of rank two. We also show that residual nilpotence of U ( KG ) coincides with nilpotence, this being no longer true if G is infinite. We can answer partially the following question: when is G sub-normal in U ( KG )?