Work

Outer automorphisms of HNN extensions of abelian groups

Year: 2026

Type: preprint

Abstract: Let $G$ be a commensurating HNN extension of a finitely generated free abelian group. We characterise when $\mathrm{Out}(G)$ is finitely generated and derive structural information about the group. We give soluble and non-soluble examples of commensurating HNN extensions of finitely generated free abelian groups with outer automorphism group not finitely generated.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28750

Authors: Andrew, Naomi, Hughes, Sam, Valiunas, Motiejus

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Rheinische Friedrich-Wilhelms-Universität Bonn, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, G591746060

OpenAlex ID: W7223214735

Cites: 71

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Related to: 10