Original scientific paper

https://doi.org/10.3336/gm.48.1.08

Commuting automorphisms of some finite groups

S. Fouladi ; Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Ave., Tehran 1561836314 , Iran
R. Orfi ; Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran

Abstract

Let G be a group. An automorphism α of G is called a commuting automorphism if xxα=xα x for all x G. We denote the set of all commuting automorphisms of G by A(G). Moreover a group G is called an AC-group if the centralizer of every non-central element of G is abelian. In this paper we show that A(G) is a subgroup of the automorphism group of G for all finite AC-groups, p-groups of maximal class, and metacyclic p-groups.

Keywords

Commuting automorphisms; AC-groups; minimal non-abelian p-groups; metacyclic p-groups; p-groups of maximal class

Hrčak ID:

103317

URI

https://hrcak.srce.hr/103317

Publication date:

4.6.2013.

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