4 papers · 1 filter
-groups and free constructions
Omar Al-Raisi, Mohammad Shahryari
Let $\X$ be a variety of groups. A group is $\CSX$ if its maximal $\X$-subgroups are malnormal. We prove that the amalgamated free product of two $\CSX$-groups with a malnormal…
On varieties where implies
Omar Al-Raisi, Mohammad Shahryari
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 m…
On 2-dimensional invariant subspaces of matrices
Omar Al-Raisi, Mohammad Shahryari
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 algebr…
On -transitive groups and conjugate separable -subgroups
Omar Al-Raisi, Mohammad Shahryari
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 thes…