Twisted conjugacy in $BS(n, 1)$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918116074717184 |
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| author | Mitra, Oorna Roy, Mallika Ventura, Enric |
| author_facet | Mitra, Oorna Roy, Mallika Ventura, Enric |
| contents | In this article, we solve the twisted conjugacy problem for solvable Baumslag--Solitar groups $BS(n,1)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(n,1)$ and an automorphism $φ\in \Aut(BS(n,1))$, decides whether $v=(wφ)^{-1} u w$ for some $w\in BS(n,1)$. Also we prove that the automorphism group $\Aut(BS(n,1))$ is orbit decidable -- given two words on the generators $u,v\in F(X)$, decide whether the corresponding elements $u,v\in G$ can be mapped to each other by some automorphism in $\Aut(BS(n,1))$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_04397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted conjugacy in $BS(n, 1)$ Mitra, Oorna Roy, Mallika Ventura, Enric Group Theory Primary 20F10 In this article, we solve the twisted conjugacy problem for solvable Baumslag--Solitar groups $BS(n,1)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(n,1)$ and an automorphism $φ\in \Aut(BS(n,1))$, decides whether $v=(wφ)^{-1} u w$ for some $w\in BS(n,1)$. Also we prove that the automorphism group $\Aut(BS(n,1))$ is orbit decidable -- given two words on the generators $u,v\in F(X)$, decide whether the corresponding elements $u,v\in G$ can be mapped to each other by some automorphism in $\Aut(BS(n,1))$. |
| title | Twisted conjugacy in $BS(n, 1)$ |
| topic | Group Theory Primary 20F10 |
| url | https://arxiv.org/abs/2508.04397 |