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Ricerche di Matematica

, Volume 68, Issue 2, pp 899–904 | Cite as

On commuting automorphisms of finite groups

  • Pradeep KumarEmail author
Article
  • 25 Downloads

Abstract

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(nq) for \(n = 3\) or \(q >n\), PSL(2, q) and ZM-groups are A-groups.

Keywords

Commuting automorphism Direct product General linear group Projective special linear group 

Mathematics Subject Classification

20F28 

Notes

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Copyright information

© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  1. 1.Department of MathematicsCentral University of South BiharGayaIndia

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