Conjugacy in a family of free-by-cyclic groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909632259162112 |
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| author | Bridson, Martin R. Riley, Timothy R. Sale, Andrew W. |
| author_facet | Bridson, Martin R. Riley, Timothy R. Sale, Andrew W. |
| contents | We analyse the geometry and complexity of the conjugacy problem in a family of free-by-cyclic groups $H_m=F_m\rtimes\mathbb{Z}$ where the defining free-group automorphism is positive and polynomially growing. We prove that the conjugator length function of $H_m$ is linear, and describe polynomial-time solutions to the conjugacy problem and conjugacy search problem in $H_m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugacy in a family of free-by-cyclic groups Bridson, Martin R. Riley, Timothy R. Sale, Andrew W. Group Theory 20F65, 20F10 We analyse the geometry and complexity of the conjugacy problem in a family of free-by-cyclic groups $H_m=F_m\rtimes\mathbb{Z}$ where the defining free-group automorphism is positive and polynomially growing. We prove that the conjugator length function of $H_m$ is linear, and describe polynomial-time solutions to the conjugacy problem and conjugacy search problem in $H_m$. |
| title | Conjugacy in a family of free-by-cyclic groups |
| topic | Group Theory 20F65, 20F10 |
| url | https://arxiv.org/abs/2506.01248 |