Edge Inversions in $(P_k)$-closed Groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917224888926208 |
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| author | Hampshire, Kirwin Lehner, Florian Wood, Andrew |
| author_facet | Hampshire, Kirwin Lehner, Florian Wood, Andrew |
| contents | We construct $(P_2)$-closed groups acting on $T_3$ in which all edge inversions have infinite order. This provides a negative answer to a question posed by Tornier. We also construct a family of $(P_2)$-closed groups for which the smallest order of an edge inversion is an arbitrarily high finite number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18982 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Edge Inversions in $(P_k)$-closed Groups Hampshire, Kirwin Lehner, Florian Wood, Andrew Group Theory Combinatorics We construct $(P_2)$-closed groups acting on $T_3$ in which all edge inversions have infinite order. This provides a negative answer to a question posed by Tornier. We also construct a family of $(P_2)$-closed groups for which the smallest order of an edge inversion is an arbitrarily high finite number. |
| title | Edge Inversions in $(P_k)$-closed Groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2601.18982 |