Automorphism groups of covering groups

TL;DR

This paper presents a formula linking the sizes of automorphism groups of finite groups and their covering groups, advancing understanding of their structural relationships.

Contribution

It introduces a new formula that explicitly relates automorphism group orders of finite groups to those of their covering groups.

Findings

Derived a formula connecting automorphism group orders

Provides insights into the structure of covering groups

Enhances understanding of automorphism group relationships

Abstract

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.