On a question of Bumagin and Wise

TL;DR

This paper constructs a continuum of finitely generated, residually finite groups with pairwise non-isomorphic, non-recursively-presentable outer automorphism groups, providing the first such examples in group theory.

Contribution

It introduces the first known examples of residually finite groups with outer automorphism groups that are non-recursively-presentable and pairwise non-isomorphic.

Findings

Constructed a continuum of such groups.

Outer automorphism groups are non-recursively-presentable.

Groups are finitely generated and residually finite.

Abstract

Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise non-isomorphic finitely generated, non-recursively-presentable groups. These are the first examples of such residually finite groups.