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

Author:

Gonçalves Jairo Z.

Abstract

AbstractLet 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)?

Publisher

Canadian Mathematical Society

Subject

General Mathematics

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