English

Geodesic growth in virtually abelian groups

Group Theory 2020-12-15 v4

Abstract

We show that the geodesic growth function of any finitely generated virtually abelian group is either polynomial or exponential; and that the geodesic growth series is holonomic, and rational in the polynomial growth case. In addition, we show that the language of geodesics is blind multicounter.

Keywords

Cite

@article{arxiv.1908.07294,
  title  = {Geodesic growth in virtually abelian groups},
  author = {Alex Bishop},
  journal= {arXiv preprint arXiv:1908.07294},
  year   = {2020}
}

Comments

23 pages, 1 figure, improved readability

R2 v1 2026-06-23T10:52:01.823Z