Endo-Twisted Conjugacy and Outer Fixed Points in Solvable Baumslag--Solitar Groups
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908827954184192 |
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| author | Roy, Mallika |
| author_facet | Roy, Mallika |
| contents | In this article, we solve the twisted conjugacy problem with respect to endomorphisms for solvable Baumslag--Solitar groups $BS(1,n)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(1,n)$ and an endomorphism $ψ\in End(BS(1,n))$, decides whether $v=(xψ)^{-1} u x$ for some $x\in BS(1,n)$. Also, we connect the outer fixed points of a given endomorphism $ψ$ with $φ$-twisted conjugacy problem for two words $u, v \in BS(1,n)$, where $φ\in End(BS(1,n))$ and $u, v$ depend on $ψ$. Furthermore, we define the weakly (outer) fixed points and discuss its interplay with the endo-twisted conjugacy problem in $BS(1, n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11031 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Endo-Twisted Conjugacy and Outer Fixed Points in Solvable Baumslag--Solitar Groups Roy, Mallika Group Theory 20F10 In this article, we solve the twisted conjugacy problem with respect to endomorphisms for solvable Baumslag--Solitar groups $BS(1,n)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(1,n)$ and an endomorphism $ψ\in End(BS(1,n))$, decides whether $v=(xψ)^{-1} u x$ for some $x\in BS(1,n)$. Also, we connect the outer fixed points of a given endomorphism $ψ$ with $φ$-twisted conjugacy problem for two words $u, v \in BS(1,n)$, where $φ\in End(BS(1,n))$ and $u, v$ depend on $ψ$. Furthermore, we define the weakly (outer) fixed points and discuss its interplay with the endo-twisted conjugacy problem in $BS(1, n)$. |
| title | Endo-Twisted Conjugacy and Outer Fixed Points in Solvable Baumslag--Solitar Groups |
| topic | Group Theory 20F10 |
| url | https://arxiv.org/abs/2602.11031 |