On class preserving automorphisms of groups of order 32

TL;DR

This paper investigates automorphisms that preserve conjugacy classes in groups of order 32, revealing that only two specific groups possess non-inner class preserving automorphisms.

Contribution

It identifies the exact groups of order 32 with non-inner class preserving automorphisms, advancing understanding of automorphism structures in small finite groups.

Findings

Only two groups of order 32 have non-inner class preserving automorphisms.

Most groups of order 32 have automorphisms that are all inner.

The paper characterizes the automorphism groups of these specific groups.

Abstract

We study class preserving automorphisms of groups of order thirty two and prove that only two groups have non-inner class preserving automorphisms.