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

Published online by Cambridge University Press:  20 November 2018

Jairo Z. Gonçalves
Jairo Z. Gonçalves*
Affiliation:
Instituto de Matemática e Estatstica, Universidade de Săo Paulo, Brasil
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Abstract

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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)?

Keywords

16A2616A4020C0520E0520E25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 365 - 370
Copyright
Copyright © Canadian Mathematical Society 1984

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