arXiv subjects

Mohammad Shahryari

Publications and source records attributed to Mohammad Shahryari.

10 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↗

arXiv2021

Nullstellensatz for relative existentially closed groups

We prove that in every variety of $G$-groups, every $G$-existentially closed element satisfies nullstellensatz for finite consistent systems of equations. This will generalize {\bf Theorem G} of \cite{BMR1}. As a result we see that every pair of $G$-existentially closed elements in an arbitrary variety of $G$-groups generate the same quasi-variety and if both of them are $q_ω$-compact, they are geometrically equivalent.

math.GR↗

arXiv2017

Hall bases for free Leibniz algebras

The aim of this article is to introduce Hall bases of free Leibniz algebras. We modify the classical notion of Hall bases for free Lie algebras in order to provide the similar construction for the case of Leibniz algebras.

math.RA↗

arXiv2010

Relative symmetric polynomials and money change problem

This article is devoted to the number of non-negative solutions of the linear Diophantine equation $$ a_1t_1+a_2t_2+... a_nt_n=d, $$ where $a_1, ..., a_n$, and $d$ are positive integers. We obtain a relation between the number of solutions of this equation and characters of the symmetric group, using {\em relative symmetric polynomials}. As an application, we give a necessary and sufficient condition for the space of the relative symmetric polynomials to be non-zero.

math.CO↗

arXiv2010

On the Automorphisms and Representations of Polyadic Groups

Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{θ, b}(G, \cdot)$, we obtain a complete description of automorphisms and representations of $(G,f)$ in terms of automorphisms and representations of the binary group $(G, \cdot)$.

math.RT↗

arXiv2010

A Note on Derivations of Lie Algebras

In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D}d(L) $$ for some $n\geq 1$, is necessarily solvable. As a result, if $L$ has a derivation $d:L\to L$, such that $L^n\subseteq d(L)$, for some $n\geq 1$, then $L$ is solvable.

math.RT↗

arXiv2010

Representations of Finite Polyadic Groups

We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite groups to the case of polyadic groups.

math.RT↗

arXiv2010

Representation Theory of Polyadic Groups

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

math.RT↗