English

Rational Growth in Virtually Abelian Groups

Group Theory 2019-09-12 v2

Abstract

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

Keywords

Cite

@article{arxiv.1808.06371,
  title  = {Rational Growth in Virtually Abelian Groups},
  author = {Alex Evetts},
  journal= {arXiv preprint arXiv:1808.06371},
  year   = {2019}
}

Comments

36 pages. Updated according to referee's suggestions. To appear in Illinois Journal of Mathematics

R2 v1 2026-06-23T03:38:08.514Z