Sections of Submonoids of Nilpotent Groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913367225008128 |
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| author | Shafrir, Doron |
| author_facet | Shafrir, Doron |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sections of Submonoids of Nilpotent Groups Shafrir, Doron Group Theory Formal Languages and Automata Theory 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. |
| title | Sections of Submonoids of Nilpotent Groups |
| topic | Group Theory Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2405.18409 |