arXiv subjects

Omar Al-Raisi

Publications and source records attributed to Omar Al-Raisi.

3 recordsLinked to original sources

arXiv2026

On varieties where $\mathrm{CS}\mathfrak{X}$ implies $\mathfrak{X}\mathrm{T}$

In our previous work \cite{Omar-Shah2}, we initiated the study of $\CSX$- and $\XT$-groups associated with a fixed variety $\X$. A group belongs to the former class if all of its maximal $\X$-subgroups are malnormal, and to the latter if any two $\X$-subgroups with nontrivial intersection generate an $\X$-subgroup. In general, $\CSX$ does not imply $\XT$, however as shown in \cite{Omar-Shah2}, some varieties do satisfy this implication. In this article, we provide additional examples of varieties for which $\CSX$ implies $\XT$.

math.GR↗

arXiv2026

On 2-dimensional invariant subspaces of matrices

We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of matrices with entries in the ring Mat_2(F) and 2-dimensional invariant subspaces of matrices with entries in the field F.

math.RA↗

arXiv2026

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

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 $\X$.

math.GR↗