On the outer automorphism groups of finitely generated, residually finite groups

TL;DR

This paper investigates which groups can be realized as outer automorphism groups of finitely generated, residually finite groups, providing partial answers for recursively presentable groups.

Contribution

It offers new insights into the realization problem of outer automorphism groups for a broad class of groups, advancing understanding in group theory.

Findings

Partial positive answer for recursively presentable groups

Clarification of conditions under which groups can be outer automorphism groups

Progress towards solving Bumagin-Wise's realization question

Abstract

Bumagin-Wise posed the question of whether every countable group can be realised as the outer automorphism group of a finitely generated, residually finite group. We give a partial answer to this problem for recursively presentable groups.