On a theorem of Ledermann and Neumann

TL;DR

This paper provides a concise, self-contained proof of a theorem by Ledermann and Neumann, establishing that only finitely many finite groups have a specified number of automorphisms, and discusses related historical conjectures.

Contribution

It offers a new, simplified proof of a key theorem about finite groups and automorphisms, and reviews the historical context of related conjectures.

Findings

Finite groups with a given number of automorphisms are finite in number.

The proof is concise and self-contained, simplifying previous approaches.

Discussion of historical conjectures related to automorphism counts.

Abstract

We give a short and self-contained proof of a theorem of Ledermann and Neumann stating that there are only finitely many finite groups with a given number of automorphisms. We also discuss the history of related conjectures.