The probability of an automorphism fixing a subgroup element of a finite group

Abstract

In 1975, Sherman introduced the probability of an automorphism of a finite group, which fixes an arbitrary element of the group. In this paper we introduce a new probability concept, namely the probability of an automorphism of a given finite group such that it fixes a subgroup element of the group. Among other results, we construct some upper and lower bounds for both probabilities. © 2011 World Scientific Publishing Company.