New classes of groups which are equational domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913313328201728 |
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| author | Raisi, O. Al Shahryari, M. |
| author_facet | Raisi, O. Al Shahryari, M. |
| contents | A group is CSA, if all of its maximal abelian subgroups are malnormal. It is known that every non-abelian CSA group is an equational domain. We generalize this result in two directions: we show that for a non-nilpotent group $G$ and a fixed positive integer $k$, if all maximal elements in the set of class $k$ nilpotent subgroups of $G$ are malnormal, then $G$ is an equational domain. Also, we prove that if a group $G$ is not locally nilpotent and if every maximal locally nilpotent subgroup of $G$ is malnormal, then $G$ is an equational domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New classes of groups which are equational domains Raisi, O. Al Shahryari, M. Group Theory 20F70 A group is CSA, if all of its maximal abelian subgroups are malnormal. It is known that every non-abelian CSA group is an equational domain. We generalize this result in two directions: we show that for a non-nilpotent group $G$ and a fixed positive integer $k$, if all maximal elements in the set of class $k$ nilpotent subgroups of $G$ are malnormal, then $G$ is an equational domain. Also, we prove that if a group $G$ is not locally nilpotent and if every maximal locally nilpotent subgroup of $G$ is malnormal, then $G$ is an equational domain. |
| title | New classes of groups which are equational domains |
| topic | Group Theory 20F70 |
| url | https://arxiv.org/abs/2401.11397 |