Twisted conjugacy in dihedral Artin groups II: Baumslag Solitar groups $\mathrm{BS}(n,n)$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929338845233152 |
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| author | Crowe, Gemma |
| author_facet | Crowe, Gemma |
| contents | In this second paper we solve the twisted conjugacy problem for even dihedral Artin groups, that is, groups with presentation $G(m) = \langle a,b \mid {}_{m}(a,b) = {}_{m}(b,a) \rangle$, where $m \geq 2$ is even, and $_{m}(a,b)$ is the word $abab\dots$ of length $m$. Similar to odd dihedral Artin groups, we prove orbit decidability for all subgroups $A \leq \mathrm{Aut}(G(m))$, which then implies that the conjugacy problem is solvable in extensions of even dihedral Artin groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted conjugacy in dihedral Artin groups II: Baumslag Solitar groups $\mathrm{BS}(n,n)$ Crowe, Gemma Group Theory Computational Complexity 20F10, 20F36 In this second paper we solve the twisted conjugacy problem for even dihedral Artin groups, that is, groups with presentation $G(m) = \langle a,b \mid {}_{m}(a,b) = {}_{m}(b,a) \rangle$, where $m \geq 2$ is even, and $_{m}(a,b)$ is the word $abab\dots$ of length $m$. Similar to odd dihedral Artin groups, we prove orbit decidability for all subgroups $A \leq \mathrm{Aut}(G(m))$, which then implies that the conjugacy problem is solvable in extensions of even dihedral Artin groups. |
| title | Twisted conjugacy in dihedral Artin groups II: Baumslag Solitar groups $\mathrm{BS}(n,n)$ |
| topic | Group Theory Computational Complexity 20F10, 20F36 |
| url | https://arxiv.org/abs/2404.04705 |