Photo by papaioannou_kostas from unsplash
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… Click to show full abstract
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.
Keywords:
autocommuting probability;
probability;
group autocommuting;
finite group;
probability finite
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!