A virtually nilpotent group whose Green series is not D-finite

2024/09/20 by Corentin Bodart, Bodart, Corentin
Mathematics · Computer Science · #Rings, Modules, and Algebras #Advanced Algebra and Logic #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2409.13395

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 D-finite. The proof relies on an arithmetical miracle, and the study of the subword complexity of a multiplicative sequence coming out of it.

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