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arXiv · 2610.28750

Outer automorphisms of HNN extensions of abelian groups

Naomi Andrew·Sam Hughes·Motiejus Valiunas
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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.

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Naomi Andrew, Sam Hughes, Motiejus Valiunas. 2026-10-20. Outer automorphisms of HNN extensions of abelian groups. https://arxiv.org/abs/2610.28750

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