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PreprintarXiv licencearXiv

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 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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Cite

BibTeXRIS
BibTeX
@misc{andrew2026outer,
  title = {{Outer automorphisms of HNN extensions of abelian groups}},
  author = {Naomi Andrew and Sam Hughes and Motiejus Valiunas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28750},
  eprint = {2610.28750},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28750},
}
RIS
TY  - UNPB
TI  - Outer automorphisms of HNN extensions of abelian groups
AU  - Naomi Andrew
AU  - Sam Hughes
AU  - Motiejus Valiunas
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28750
UR  - https://arxiv.org/abs/2610.28750
AB  - Let G be a commensurating HNN extension of a finitely generated free abelian group. We characterise when 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.
ER  -