A virtually nilpotent group whose Green series is not D-finite
Group Theory
2026-04-29 v2 Combinatorics
Number Theory
Abstract
We provide the first example of virtually nilpotent group, with a specific generating set, for which the Green series (sometimes called cogrowth series) is not -finite. The proof relies on an arithmetical miracle, and the study of the subword complexity of a multiplicative sequence coming out of it.
Cite
@article{arxiv.2409.13395,
title = {A virtually nilpotent group whose Green series is not D-finite},
author = {Corentin Bodart},
journal= {arXiv preprint arXiv:2409.13395},
year = {2026}
}
Comments
v2: Published version taking into account referee suggestions. Slight change in title v1: 11 pages, 2 figures. Comments are welcome