# On equality of inner and absolute central automorphisms

## TL;DR

This paper investigates conditions under which the group of absolute central automorphisms of a finite p-group coincides with its inner automorphism group, providing a precise characterization.

## Contribution

It establishes necessary and sufficient conditions for the equality of Aut_l(G) and Inn(G) in finite p-groups, advancing understanding of automorphism structures.

## Key findings

- Characterization of when Aut_l(G) equals Inn(G)
- Necessary and sufficient conditions identified
- Enhanced understanding of automorphism groups in p-groups

## Abstract

Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. We give necessary and sufficient conditions on G such that Aut_l(G) = Inn(G).