May 9, 2024Open Access

Bounded Generation of Submonoids of Heisenberg Groups

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Abstract

If G is a nilpotent group and G, G has Hirsch length 1, then every f. g. submonoid of G is boundedly generated, i. e. a product of cyclic submonoids. Using a reduction of Bodart, this implies the decidability of the submonoid membership problem for nilpotent groups G where G, G has Hirsch length 2.

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Doron Shafrir (Thu,) studied this question.

synapsesocial.com/papers/68e6aec4b6db643587630f36 https://doi.org/https://doi.org/10.48550/arxiv.2405.05939

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3On decidability of the product of subgroups membership problem for nilpotent groups2024
4Bounded subgroups of relatively finitely presented groups2024
5A saturation theorem for submonoids of nilpotent groups and the Identity Problem2024

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