Autocommuting probability of a finite group

2017/02/02 by Dutta, Parama, Nath, Rajat Kanti
#20D60 #20F28 #20P05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1702.00561

Abstract

Let G be a finite group and \Aut(G) the automorphism group of G. The autocommuting probability of G, denoted by Pr(G, \Aut(G)), is the probability that a randomly chosen automorphism of G fixes a randomly chosen element of G. In this paper, we study Pr(G, \Aut(G)) through a generalization. We obtain a computing formula, several bounds and characterizations of G through Pr(G, \Aut(G)). We conclude the paper by showing that the generalized autocommuting probability of G remains unchanged under autoisoclinism.

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