Automorphisms of graphs of groups with cyclic edge groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918101752217600 |
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| author | Ascari, Dario Casals-Ruiz, Montserrat Kazachkov, Ilya |
| author_facet | Ascari, Dario Casals-Ruiz, Montserrat Kazachkov, Ilya |
| contents | We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group is virtually built from the outer automorphisms of the vertex groups (fixing some elements), the outer automorphisms of some associated generalized Baumslag-Solitar groups, and generalized twists - partial conjugations by elements in the centralizers of some elliptic elements in the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automorphisms of graphs of groups with cyclic edge groups Ascari, Dario Casals-Ruiz, Montserrat Kazachkov, Ilya Group Theory 20E08, 20F10, 20F28 We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group is virtually built from the outer automorphisms of the vertex groups (fixing some elements), the outer automorphisms of some associated generalized Baumslag-Solitar groups, and generalized twists - partial conjugations by elements in the centralizers of some elliptic elements in the group. |
| title | Automorphisms of graphs of groups with cyclic edge groups |
| topic | Group Theory 20E08, 20F10, 20F28 |
| url | https://arxiv.org/abs/2507.16489 |