Geodesic growth in virtually abelian groups

Alex Bishop

doi:10.1016/j.jalgebra.2020.12.003

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arXiv · 1908.07294

Geodesic growth in virtually abelian groups

Alex Bishop

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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.

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Alex Bishop. 2019-08-20. Geodesic growth in virtually abelian groups. https://doi.org/10.1016/j.jalgebra.2020.12.003

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