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| Format: | Preprint |
| Veröffentlicht: |
2021
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2112.01912 |
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| _version_ | 1866917139447808000 |
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| author | Duda, Karol |
| author_facet | Duda, Karol |
| contents | We prove that torsion subgroups of groups defined by C(6), C(4)-T(4) or C(3)-T(6) small cancellation presentations are finite cyclic groups. This follows from a more general result on the existence of fixed points for locally elliptic (every element fixes a point) actions of groups on simply connected small cancellation complexes. We present an application concerning automatic continuity. We observe that simply connected C(3)-T(6) complexes may be equipped with a CAT(0) metric. This allows us to get stronger results on locally elliptic actions in that case. It also implies that the Tits Alternative holds for groups acting on simply connected C(3)-T(6) small cancellation complexes with a bound on the order of cell stabilisers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_01912 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Torsion subgroups of small cancellation groups Duda, Karol Group Theory We prove that torsion subgroups of groups defined by C(6), C(4)-T(4) or C(3)-T(6) small cancellation presentations are finite cyclic groups. This follows from a more general result on the existence of fixed points for locally elliptic (every element fixes a point) actions of groups on simply connected small cancellation complexes. We present an application concerning automatic continuity. We observe that simply connected C(3)-T(6) complexes may be equipped with a CAT(0) metric. This allows us to get stronger results on locally elliptic actions in that case. It also implies that the Tits Alternative holds for groups acting on simply connected C(3)-T(6) small cancellation complexes with a bound on the order of cell stabilisers. |
| title | Torsion subgroups of small cancellation groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2112.01912 |