The Bass-Jiang group for automorphism-induced HNN-extensions

TL;DR

This paper introduces a framework using the Bass-Jiang group to construct groups with complex outer automorphism groups, addressing a question about finitely presented, residually finite groups.

Contribution

It develops a new framework based on the Bass-Jiang group for automorphism-induced HNN-extensions, enabling the construction of groups with pathological outer automorphism groups.

Findings

Constructed groups with complex outer automorphism groups

Provided new insights into automorphism groups of finitely presented groups

Addressed a question of Bumagin--Wise on residual finiteness

Abstract

We use the Bass--Jiang group for automorphism-induced HNN-extensions to build a framework for the construction of tractable groups with pathological outer automorphism groups. We apply this framework to a strong form of a question of Bumagin--Wise on the outer automorphism groups of finitely presented, residually finite groups.