Twisted conjugacy in dihedral Artin groups I: Torus Knot groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908380796289024 |
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| author | Crowe, Gemma |
| author_facet | Crowe, Gemma |
| contents | In this paper we provide an alternative solution to a result by Juhász that the twisted conjugacy problem for odd dihedral Artin groups is solvable, that is, groups with presentation $G(m) = \langle a,b \; | \; _{m}(a,b) = {}_{m}(b,a) \rangle$, where $m\geq 3$ is odd, and $_{m}(a,b)$ is the word $abab \dots$ of length $m$, is solvable. Our solution provides an implementable linear time algorithm, by considering an alternative group presentation to that of a torus knot group, and working with geodesic normal forms. An application of this result is that the conjugacy problem is solvable in extensions of odd dihedral Artin groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted conjugacy in dihedral Artin groups I: Torus Knot groups Crowe, Gemma Group Theory Computational Complexity 20F10, 20F36 In this paper we provide an alternative solution to a result by Juhász that the twisted conjugacy problem for odd dihedral Artin groups is solvable, that is, groups with presentation $G(m) = \langle a,b \; | \; _{m}(a,b) = {}_{m}(b,a) \rangle$, where $m\geq 3$ is odd, and $_{m}(a,b)$ is the word $abab \dots$ of length $m$, is solvable. Our solution provides an implementable linear time algorithm, by considering an alternative group presentation to that of a torus knot group, and working with geodesic normal forms. An application of this result is that the conjugacy problem is solvable in extensions of odd dihedral Artin groups. |
| title | Twisted conjugacy in dihedral Artin groups I: Torus Knot groups |
| topic | Group Theory Computational Complexity 20F10, 20F36 |
| url | https://arxiv.org/abs/2403.16671 |