# A survey on the Non-inner Automorphism Conjecture

## TL;DR

This survey reviews the current state of research on the non-inner automorphism conjecture, which posits that all finite non-abelian p-groups possess a non-inner automorphism of order p.

## Contribution

It compiles and summarizes known results and progress related to the long-standing conjecture in group theory.

## Key findings

- Summary of known results on the conjecture
- Identification of cases where the conjecture holds
- Open problems and directions for future research

## Abstract

In this survey article, we try to summarize the known results towards the long-standing non-inner automorphism conjecture, which states that every finite non-abelian $p$-group has a non-inner automorphism of order $p$.