arXiv subjects

Samuel H. Dalalyan

Publications and source records attributed to Samuel H. Dalalyan.

3 recordsLinked to original sources

arXiv2015

Structures induced on transversals to a subgroup of a group and hypergroups over the group

On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the quotient-group of the given group with respect to the normal subgroup. The category of the hypergroups over the group contains as subcategories the category of groups, the category of linear spaces, the category of fields.

math.GR↗

arXiv2015

An algorithm for determining the irreducible polynomials over finite fields

We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.

math.NT↗

arXiv2014

Hypergroups over the group and generalizations of Schreier's theorem on group extensions

Let $H$ be a group, $m$ be a positive integer, $Ext_m H$ be the set of all isomorphic in $G$ classes of group monomorphisms $φ: H \rightarrow G$ such that index of $φ(H)$ in $G$ is $m$. The main goal of this paper is to describe the elements of $Ext_m H$ in terms of a new concept of hypergroups over the group. The obtained result is a very broad generalization of the Schreier theorem (1926). As an application, a series of intermediate generalizations is obtained; particularly, a description of the set $Ext (H, Q)$ of isomorphic classes of all extensions of a noncommutative group $H$ by $Q$.

math.GR↗