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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Group rings whose symmetric elements
are Lie nilpotent


Author: Gregory T. Lee
Journal: Proc. Amer. Math. Soc. 127 (1999), 3153-3159
MSC (1991): Primary 20C07, 16S34, 17B30
Published electronically: May 4, 1999
MathSciNet review: 1641124
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $FG$ be the group ring of a group $G$ over a field $F$, with characteristic different from $2$. Let $\ast $ denote the natural involution on $FG$ sending each group element to its inverse. Denote by $(FG)^{+}$ the set of symmetric elements with respect to this involution. A paper of Giambruno and Sehgal showed that provided $G$ has no $2$-elements, if $(FG)^{+}$ is Lie nilpotent, then so is $FG$. In this paper, we determine when $(FG)^{+}$ is Lie nilpotent, if $G$ does contain $2$-elements.


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Additional Information

Gregory T. Lee
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: glee@vega.math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05155-2
PII: S 0002-9939(99)05155-2
Received by editor(s): January 26, 1998
Published electronically: May 4, 1999
Additional Notes: The author is supported in part by a Province of Alberta Graduate Fellowship.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society