Bounded Generation of Submonoids of Heisenberg Groups
Group Theory
2024-05-10 v1 Discrete Mathematics
Formal Languages and Automata Theory
Abstract
If is a nilpotent group and has Hirsch length , then every f.g. submonoid of 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 where has Hirsch length .
Cite
@article{arxiv.2405.05939,
title = {Bounded Generation of Submonoids of Heisenberg Groups},
author = {Doron Shafrir},
journal= {arXiv preprint arXiv:2405.05939},
year = {2024}
}