# The automorphism group of a nonsplit metacyclic 2-group

## TL;DR

This paper fully characterizes the automorphism groups of nonsplit metacyclic 2-groups, filling a gap in the understanding of automorphism groups for metacyclic p-groups.

## Contribution

It provides a complete description of automorphism groups for a class of nonsplit metacyclic 2-groups, advancing the classification of automorphisms in these groups.

## Key findings

- Determined the structure of automorphism groups for nonsplit metacyclic 2-groups.
- Completed the classification of automorphism groups for all metacyclic p-groups.
- Extended previous work to include nonsplit cases.

## Abstract

We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$-groups.