Bounded Generation of Submonoids of Heisenberg Groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866909196856852480 |
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| author | Shafrir, Doron |
| author_facet | Shafrir, Doron |
| contents | 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 $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounded Generation of Submonoids of Heisenberg Groups Shafrir, Doron Group Theory Discrete Mathematics Formal Languages and Automata Theory 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 $2$. |
| title | Bounded Generation of Submonoids of Heisenberg Groups |
| topic | Group Theory Discrete Mathematics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2405.05939 |