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Group algebras with an Engel group of units

Part of: Representation theory of groups Rings and algebras arising under various constructions Conditions on elements

Published online by Cambridge University Press:  09 April 2009

A. Bovdi
A. Bovdi
Affiliation:
University of Debrecen, 4010 Debrecen, Hungary, e-mail: bodibela@math.klte.hu
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Abstract

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Let F be a field of characteristic p and G a group containing at least one element of order p. It is proved that the group of units of the group algebra FG is a bounded Engel group if and only if FG is a bounded Engel algebra, and that this is the case if and only if G is nilpotent and has a normal subgroup H such that both the factor group G/H and the commutator subgroup H′ are finite p–groups.

Keywords

Group algebragroup of unitsn–Engel groupsEngel groups.

MSC classification

Secondary: 16S34: Group rings , Laurent polynomial rings 16U60: Units, groups of units 20C05: Group rings of finite groups and their modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 2 , April 2006 , pp. 173 - 178
Copyright
Copyright © Australian Mathematical Society 2006

References

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