Twisted conjugacy growth series of virtually abelian groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911046149603328 |
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| author | Evetts, Alex Lathouwers, Maarten |
| author_facet | Evetts, Alex Lathouwers, Maarten |
| contents | We initiate the study of the \emph{twisted conjugacy growth series} of a finitely generated group, the formal power series associated to the twisted conjugacy growth function. Our main result is that, for a virtually abelian group, this series is always an explicitly computable $\mathbb{N}$-rational function. As a corollary, we obtain a similar result for the relative growth series of a twisted conjugacy class in a virtually abelian group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted conjugacy growth series of virtually abelian groups Evetts, Alex Lathouwers, Maarten Group Theory 20F65, 20F10 We initiate the study of the \emph{twisted conjugacy growth series} of a finitely generated group, the formal power series associated to the twisted conjugacy growth function. Our main result is that, for a virtually abelian group, this series is always an explicitly computable $\mathbb{N}$-rational function. As a corollary, we obtain a similar result for the relative growth series of a twisted conjugacy class in a virtually abelian group. |
| title | Twisted conjugacy growth series of virtually abelian groups |
| topic | Group Theory 20F65, 20F10 |
| url | https://arxiv.org/abs/2410.18753 |