Twisted conjugacy growth series of virtually abelian groups

Fuente: arXiv
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Main Authors: Evetts, Alex, Lathouwers, Maarten
Format: Preprint
Published: 2024
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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