Bounded Generation of Submonoids of Heisenberg Groups
<|reference_start|>Bounded Generation of Submonoids of Heisenberg Groups: 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 $2$.<|reference_end|>
@article{shafrir2024bounded,
    title={Bounded Generation of Submonoids of Heisenberg Groups},
    author={Doron Shafrir},
    journal={arXiv preprint arXiv:2405.05939},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.05939},
    primaryClass={math.GR cs.DM cs.FL}
}