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Rational Growth in Virtually Abelian Groups

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arxiv 1808.06371 v2 pith:EJT33IA3 submitted 2018-08-20 math.GR

Alex Evetts This is my paper · ORCID
classification math.GR
keywords growsrationallyabeliansubgroupvirtuallychoiceclassesconjugacy
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abstract

We show that any subgroup of a finitely generated virtually abelian group $G$ grows rationally relative to $G$, that the set of right cosets of any subgroup of $G$ grows rationally, and that the set of conjugacy classes of $G$ grows rationally. These results hold regardless of the choice of finite weighted generating set for $G$.

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  1. The conjugacy growth of the soluble Baumslag-Solitar groups

    math.GR 2019-08 accept novelty 7.0 of 10

    For each k at least 2, the conjugacy growth series of BS(1,k) with respect to the standard generating set is transcendental, and its growth rate equals the standard growth rate.

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