Rational growth in virtually abelian groups

Alex Evetts

doi:10.1215/00192082-8011497

Rational growth in virtually abelian groups

Alex Evetts

Pure Mathematics

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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.

Original language	English
Journal	Illinois Journal of Mathematics
Volume	63
Issue number	4
Early online date	19 Nov 2019
DOIs	https://doi.org/10.1215/00192082-8011497
Publication status	Published - 1 Dec 2019

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10.1215/00192082-8011497

1808.06371Accepted author manuscript, 362 KB

https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-63/issue-4/Rational-growth-in-virtually-abelian-groups/10.1215/00192082-8011497.full

Cite this

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AB - 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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JO - Illinois Journal of Mathematics

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Rational growth in virtually abelian groups

Abstract

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