Algebraic and arithmetic properties of the cogrowth sequence of nilpotent groups

Igor Pak; David Soukup

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arXiv · 2210.09419

Algebraic and arithmetic properties of the cogrowth sequence of nilpotent groups

Igor Pak·David Soukup

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Abstract

We prove that congruences of the cogrowth sequence in a unitriangular group UT$(m, \Bbb Z)$ are undecidable. This is in contrast with abelian groups, where the congruences of the cogrowth sequence are decidable. As an application, we conclude that there is no algorithm to present the cogrowth series as the diagonal of a rational function.

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BibTeX RIS

Igor Pak, David Soukup. 2022-10-17. Algebraic and arithmetic properties of the cogrowth sequence of nilpotent groups. https://arxiv.org/abs/2210.09419

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