Autocommuting probability of a finite group |
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Authors: | Parama Dutta |
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Institution: | Department of Mathematical Sciences, Tezpur University, Tezpur, Assam, India |
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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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Keywords: | Autocommuting probability autoisoclinism automorphism group |
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