Minimal odd order automorphism groups

TL;DR

This paper proves that the smallest non-trivial automorphism group of odd order for a finite group has order 3^7, establishing a minimal bound in group theory.

Contribution

It identifies the minimal order of a non-trivial automorphism group of odd order as 3^7, providing a new lower bound in the classification of automorphism groups.

Findings

3^7 is the smallest order of a non-trivial odd automorphism group

Established a lower bound for automorphism group orders in finite groups

Contributed to the understanding of automorphism group structures

Abstract

We show that 3^7 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.