A virtually nilpotent group whose Green series is not D-finite
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 [Formula: see text]-finite. The proof relies on an arithmetical miracle, and the study of the subword complexity of a multiplicative sequence coming out of it.
Authors
- Corentin Bodart (ORCID: https://orcid.org/0000-0001-9911-7062)
Institutions
- University of Oxford (GB)
Publication Details
- Journal
- International Journal of Algebra and Computation
- Published
- 2025-11-21
- DOI
- https://doi.org/10.1142/s0218196726500074
- Primary Topic
- semigroups and automata theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00