Abstract
Let G be a group and let F be a field of characteristic different from 2. Denote by (FG) + the set of symmetric elements and by U +(FG) the set of symmetric units of the group algebra FG, with respect to the canonical involution on FG sending each group element to its inverse. In this article, we give some lower and upper bounds on the Lie nilpotency index of (FG) + and the nilpotency class of U +(FG); furthermore, we classify the groups for which these bounds are achieved.
Original language | English |
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Pages (from-to) | 4283-4294 |
Number of pages | 12 |
Journal | Communications in Algebra |
Volume | 40 |
Issue number | 11 |
DOIs | |
Publication status | Published - Nov 2012 |
Externally published | Yes |
Keywords
- Group ring
- Involution
- Lie nilpotency index
- Nilpotency class
ASJC Scopus subject areas
- Algebra and Number Theory