Sections of Submonoids of Nilpotent Groups
<|reference_start|>Sections of Submonoids of Nilpotent Groups: We show that every product of f.g.\ submonoids of a group $G$ is a section of a f.g.\ submonoid of $G{\times}H_5(\mathbb{Z})$, where $H_5(\mathbb{Z})$ is a Heisenberg group. This gives us a converse of a reduction of Bodart, and a new simple proof of the existence of a submonoid of a nilpotent group of class 2 with undecidable membership problem.<|reference_end|>
@article{shafrir2024sections,
    title={Sections of Submonoids of Nilpotent Groups},
    author={Doron Shafrir},
    journal={arXiv preprint arXiv:2405.18409},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.18409},
    primaryClass={math.GR cs.FL}
}