This article is cited in 2 papers

Groups acting on groups

M. Deaconescu^a, G. L. Walls<sup>b

a</sup> Dep. Math., Kuwait Univ., P. O. Box 5969, Safat 13060, Kuwait
^b Dep. Math., Southeastern Louisiana Univ., Hammond, LA 70403, USA

Abstract: Combinatorial methods are used to give a characterization of finite groups $G$ with $\mathrm{Aut}(G)$ Abelian and to show that if $G$ is a finite group and $\alpha$ is an automorphism of $G$, then the number of fixed points of $\alpha$ in $G$ is a multiple of the number of fixed points of $\alpha$ in $G/Z(G)$.

Keywords: finite groups, automorphisms, fixed points, orbits, Abelian automorphism groups.

UDC: 512.542

Received: 21.07.2013

 English version: Algebra and Logic, 2013, 52:5, 387–391

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