Symmetric units satisfying a group identity
- 作者：Ann Dooms ; Manuel Ruiz
- 关键词：Group algebra ; Unit group ; Group identities ; Symmetric units
- 刊名：Journal of Algebra
- 出版年：2007
- 期刊代码：69_00218693
- 类别：mt
- 出版时间：15 February 2007
- 卷：308
- 期：2
- 页码：742-750
- 文件大小：135 K
摘要
Let K be an infinite field of characteristic p≠2, 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.