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Group algebras whose symmetric and skew elements are Lie solvable.
- Source :
-
Forum Mathematicum . 2009, Vol. 21 Issue 4, p661-671. 11p. - Publication Year :
- 2009
-
Abstract
- Let FG be the group algebra of a group G without 2-elements over a field F of characteristic p ≠ 2 endowed with the canonical involution induced from the map g ↦ g–1, g ∈ G. Let ( FG)– and ( FG)+ be the sets of skew and symmetric elements of FG, respectively, and let P denote the set of p-elements of G (with P = 1 if p = 0). In the present paper we prove that if either P is finite or G is non-torsion and ( FG)– or ( FG)+ is Lie solvable, then FG is Lie solvable. The remaining cases are also settled upon small restrictions. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*LIE algebras
*INTEGRAL theorems
*MATHEMATICS
*SUBGROUP growth
Subjects
Details
- Language :
- English
- ISSN :
- 09337741
- Volume :
- 21
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Forum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 41571583
- Full Text :
- https://doi.org/10.1515/FORUM.2009.033