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

Omar Al-Raisi; Mohammad Shahryari

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

Group Theory 2026-01-05 v1

Authors: Omar Al-Raisi , Mohammad Shahryari

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 $\X$ .

Keywords

wreath product of groups finite group theory group theory

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@article{arxiv.2601.00746,
  title  = {On $\mathfrak{X}$-transitive groups and conjugate separable $\mathfrak{X}$-subgroups},
  author = {Omar Al-Raisi and Mohammad Shahryari},
  journal= {arXiv preprint arXiv:2601.00746},
  year   = {2026}
}

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23 pages

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

Abstract

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