Bounded Generation of Submonoids of Heisenberg Groups
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 $2$.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.05939
- arXiv:
- arXiv:2405.05939
- Bibcode:
- 2024arXiv240505939S
- Keywords:
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- Mathematics - Group Theory;
- Computer Science - Discrete Mathematics;
- Computer Science - Formal Languages and Automata Theory