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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Omar Al-Raisi, M. Shahryari
DOI: 10.48550/arxiv.2601.00746
Cited by: 0

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 $\X$.

Fields of Study & Subjects

Finite Group Theory Research Geometric and Algebraic Topology Homotopy and Cohomology in Algebraic Topology

Publication details

Journal / source
arXiv (Cornell University)
Publication date
2 January 2026
Document type
Preprint