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Symmetric units satisfying a group identity
- Source :
-
Journal of Algebra . Feb2007, Vol. 308 Issue 2, p742-750. 9p. - Publication Year :
- 2007
-
Abstract
- Abstract: Let K be an infinite field of characteristic , G a locally finite group and KG its group algebra. Let denote the K-linear extension of an involution φ defined on G. In this paper we prove, under some assumptions, that if the set of φ-symmetric units of KG satisfies a group identity then KG satisfies a polynomial identity. Moreover, in case the prime radical of KG is nilpotent we characterize the groups for which the φ-symmetric units satisfy a group identity. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*GROUP identity
*FINITE groups
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 308
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 23277748
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2006.09.014