# On relative autocommutativity degree of a subgroup of a finite group

## TL;DR

This paper investigates the probability that a random automorphism fixes a random element of a subgroup in a finite group, providing new results and generalizations to deepen understanding of group automorphisms.

## Contribution

It introduces new bounds and generalizations for the autocommutativity degree of subgroups in finite groups, advancing theoretical understanding.

## Key findings

- Derived new bounds for autocommutativity degree
- Generalized existing results on automorphism fixing probabilities
- Improved understanding of automorphism actions on subgroups

## Abstract

In this paper, we consider the probability that a randomly chosen automorphism of a finite group fixes a randomly chosen element of a subgroup of that group. We obtain several new results as well as generalizations and improvements of some existing results on this probability.