7 papers
-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…
New classes of groups which are equational domains
O. Al Raisi, M. Shahryari
A group is CSA, if all of its maximal abelian subgroups are malnormal. It is known that every non-abelian CSA group is an equational domain. We generalize this result in two direct…
On conjugate separability of nilpotent subgroups
M. Shahryari
We study groups, all maximal nilpotent subgroups of class at most in which are malnormal. We show that such groups share many similar properties with the ordinary CSA groups. S…
Limits of Generalized Quaternion Groups
R. Hobbi, M. Shahryari
In the space of marked group, we determine the structure of groups which are limit points of the set of all generalized quaternion groups.