The Outer Automorphism Groups of Two-Generator One-Relator Groups with Torsion

TL;DR

This paper provides a complete classification of the outer automorphism groups for two-generator, one-relator groups with torsion, utilizing recent algorithms to determine their isomorphism classes.

Contribution

It offers a comprehensive classification and an algorithmic method to compute the outer automorphism groups for these specific groups.

Findings

Complete classification of outer automorphism groups

Algorithm to compute isomorphism classes

Application of recent algorithmic results

Abstract

The main result of this paper is a complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion. To this classification we apply recent algorithmic results of Dahmani--Guirardel, which yields an algorithm to compute the isomorphism class of the outer automorphism group of a given two-generator, one-relator group with torsion.