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arXiv · 2402.07337

A saturation theorem for submonoids of nilpotent groups and the Identity Problem

Doron Shafrir
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Abstract

If $M$ is a submonoid of a finitely generated nilpotent group $G$, and $MG'$ is a finite index subgroup of $G$, then $M$ itself is a finite index subgroup of $G$. If $MG'=G$, then $M=G$. This generalizes a well-known theorem for subgroups of finitely generated nilpotent groups. As a result, we give an algorithm for the Identity Problem in nilpotent groups.

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Doron Shafrir. 2024-02-12. A saturation theorem for submonoids of nilpotent groups and the Identity Problem. https://arxiv.org/abs/2402.07337

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