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GROUP ALGEBRAS WHOSE UNIT GROUP IS LOCALLY NILPOTENT

Part of: Representation theory of groups Special aspects of infinite or finite groups Rings and algebras arising under various constructions

Published online by Cambridge University Press:  07 May 2020

V. BOVDI Open the ORCID record for V. BOVDI [Opens in a new window]
V. BOVDI*
Affiliation:
UAEU, Math Sciences, COS, P.O. Box 15551, Al Ain, United Arab Emirates email [email protected]
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Abstract

We present a complete list of groups $G$ and fields $F$ for which: (i) the group of normalized units $V(FG)$ of the group algebra $FG$ is locally nilpotent; (ii) the set of nontrivial nilpotent elements of $FG$ is finite and nonempty, and $V(FG)$ is an Engel group.

Keywords

unit groupgroup algebralocally nilpotent groupEngel group

MSC classification

Primary: 20C05: Group rings of finite groups and their modules
Secondary: 16S34: Group rings , Laurent polynomial rings 20F45: Engel conditions 20F19: Generalizations of solvable and nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 109 , Issue 1 , August 2020 , pp. 17 - 23
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by the UAEU UPAR Grant G00002160.

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