On the isomorphism of unitary subgroups of noncommutative group algebras

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Zsolt Adam Balogh¹ 

[1] Department of Mathematical Sciences, United Arab Emirates University

关键词: Group ring;    Group of units;    Unitary subgroup;   

DOI  :  10.13069/jacodesmath.1111746

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Let $FG$ be the group algebra of a finite $p$-group $G$ over a field $F$ of characteristic $p$. Let $\cd$ be an involution of the group algebra $FG$ which arises form the group basis $G$. The upper bound for the number of non-isomorphic $\cd$-unitary subgroups is the number of conjugacy classes of the automorphism group $G$ with all the elements of order two. The upper bound is not always reached in the case when $G$ is an abelian group, but for non-abelian case the question is open. In this paper we present a non-abelian $p$-group $G$ whose group algebra $FG$ has sharply less number of non-isomorphic $\cd$-unitary subgroups than the given upper bound.

【 授权许可】

CC BY