On $\mathfrak{X}$-transitive groups and conjugate separable $\mathfrak{X}$-subgroups

Omar Al-Raisi; Mohammad Shahryari

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arXiv · 2601.00746

On $\mathfrak{X}$-transitive groups and conjugate separable $\mathfrak{X}$-subgroups

Omar Al-Raisi·Mohammad Shahryari

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Abstract

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 $\X$.

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Omar Al-Raisi, Mohammad Shahryari. 2026-01-02. On $\mathfrak{X}$-transitive groups and conjugate separable $\mathfrak{X}$-subgroups. https://arxiv.org/abs/2601.00746

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