On $\mathfrak{X}$-transitive groups and conjugate separable $\mathfrak{X}$-subgroups
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915704640372736 |
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| author | Al-Raisi, Omar Shahryari, Mohammad |
| author_facet | Al-Raisi, Omar Shahryari, Mohammad |
| contents | For a given variety of groups $\X$, we develop a systematic theory of $\CSX$-groups and $\XT$-groups, extending ideas proposed in \cite{Shah}. We analyze the interplay between these classes, describe their structural properties, and examine their connections with equational domains and residually $A$-free groups. Furthermore, we prove by elementary means that every finite $\CSX$-group lies in $\X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00746 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $\mathfrak{X}$-transitive groups and conjugate separable $\mathfrak{X}$-subgroups Al-Raisi, Omar Shahryari, Mohammad Group Theory 20E06, 20E26, 20F70 For a given variety of groups $\X$, we develop a systematic theory of $\CSX$-groups and $\XT$-groups, extending ideas proposed in \cite{Shah}. We analyze the interplay between these classes, describe their structural properties, and examine their connections with equational domains and residually $A$-free groups. Furthermore, we prove by elementary means that every finite $\CSX$-group lies in $\X$. |
| title | On $\mathfrak{X}$-transitive groups and conjugate separable $\mathfrak{X}$-subgroups |
| topic | Group Theory 20E06, 20E26, 20F70 |
| url | https://arxiv.org/abs/2601.00746 |