A saturation theorem for submonoids of nilpotent groups and the Identity Problem
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916121855131648 |
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| author | Shafrir, Doron |
| author_facet | Shafrir, Doron |
| contents | If $M$ is a submonoid of a finitely generated nilpotent group $G$, and $MG'$ is a finite index subgroup of $G$, then $M$ itself is a finite index subgroup of $G$. If $MG'=G$, then $M=G$. This generalizes a well-known theorem for subgroups of finitely generated nilpotent groups. As a result, we give an algorithm for the Identity Problem in nilpotent groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A saturation theorem for submonoids of nilpotent groups and the Identity Problem Shafrir, Doron Group Theory 20F10 (Primary) 20F18 (Secondary) If $M$ is a submonoid of a finitely generated nilpotent group $G$, and $MG'$ is a finite index subgroup of $G$, then $M$ itself is a finite index subgroup of $G$. If $MG'=G$, then $M=G$. This generalizes a well-known theorem for subgroups of finitely generated nilpotent groups. As a result, we give an algorithm for the Identity Problem in nilpotent groups. |
| title | A saturation theorem for submonoids of nilpotent groups and the Identity Problem |
| topic | Group Theory 20F10 (Primary) 20F18 (Secondary) |
| url | https://arxiv.org/abs/2402.07337 |