On commuting automorphisms of finite groups
- 25 Downloads
Let G be a group. An automorphism \(\alpha \) of G is called a commuting automorphism if \(\alpha (x)x= x \alpha (x)\) for all \(x \in G\). The set of all commuting automorphisms of G is denoted by A(G). The set A(G) does not necessarily form a subgroup of the automorphism group of G. If A(G) form a subgroup, then we say G is an A-group. In this paper, we show that the direct product of two finite A-groups is also an A-group. We also show that GL(n, q) for \(n = 3\) or \(q >n\), PSL(2, q) and ZM-groups are A-groups.
KeywordsCommuting automorphism Direct product General linear group Projective special linear group
Mathematics Subject Classification20F28