Commensurators of abelian subgroups of biautomatic groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929339680948224 |
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| author | Valiunas, Motiejus |
| author_facet | Valiunas, Motiejus |
| contents | We show that the commensurator of any finitely generated abelian subgroup $H$ in a biautomatic group centralises a finite-index subgroup of $H$. We deduce that the CAT(0) groups introduced by Leary-Minasyan are either biautomatic or cannot arise as subgroups of biautomatic groups, answering a question posed by Leary-Minasyan and generalising an analogous result for Baumslag-Solitar groups. These are the first examples of CAT(0) groups that are not subgroups of biautomatic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_13688 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Commensurators of abelian subgroups of biautomatic groups Valiunas, Motiejus Group Theory 20F10, 20E06 We show that the commensurator of any finitely generated abelian subgroup $H$ in a biautomatic group centralises a finite-index subgroup of $H$. We deduce that the CAT(0) groups introduced by Leary-Minasyan are either biautomatic or cannot arise as subgroups of biautomatic groups, answering a question posed by Leary-Minasyan and generalising an analogous result for Baumslag-Solitar groups. These are the first examples of CAT(0) groups that are not subgroups of biautomatic groups. |
| title | Commensurators of abelian subgroups of biautomatic groups |
| topic | Group Theory 20F10, 20E06 |
| url | https://arxiv.org/abs/2104.13688 |