Glasnik Matematicki, Vol. 48, No. 1 (2013), 91-96.

COMMUTING AUTOMORPHISMS OF SOME FINITE GROUPS

S. Fouladi and R. Orfi

Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
e-mail: r-orfi@araku.ac.ir

Abstract.   Let G be a group. An automorphism α of G is called a commuting automorphism if xx^α=x^α 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.

2010 Mathematics Subject Classification.   20F28, 20D15.

Key words and phrases.   Commuting automorphisms, AC-groups, minimal non-abelian p-groups, metacyclic p-groups, p-groups of maximal class.

DOI: 10.3336/gm.48.1.08

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