Autocommuting probability of a finite group

作者：Dutta Parama; Nath Rajat Kanti^*

来源：Communications in Algebra, 2018, 46(3): 961-969.

DOI：10.1080/00927872.2017.1332201

• Autocommuting probability
• autoisoclinism
• automorphism group

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.

• 出版日期2018