Group rings whose symmetric elements are Lie nilpotent
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- by Gregory T. Lee PDF
- Proc. Amer. Math. Soc. 127 (1999), 3153-3159 Request permission
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.References
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Additional Information
- Gregory T. Lee
- Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- MR Author ID: 630850
- Email: glee@vega.math.ualberta.ca
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3153-3159
- MSC (1991): Primary 20C07, 16S34, 17B30
- DOI: https://doi.org/10.1090/S0002-9939-99-05155-2
- MathSciNet review: 1641124