Mikhail Kabenyuk

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20232026

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math.GR2026

Factors in infinite groups

Mikhail Kabenyuk

Let $G$ be a group and $A \subseteq G$ a non-empty subset. A right $s$ -factor associated with $A$ is a maximal subset $U \subseteq G$ such that the product $A U$ is direct. The lower…

math.GR2026

Factors in finite groups and well-covered graphs

Mikhail Kabenyuk

We study a combinatorial property of subsets in finite groups that is analogous to the notion of independence in graphs. Given a group $G$ and a non-empty subset $A \subset G$ , we d…

math.GR2025

A Note on Lagrange Subsets of Finite Groups

Mikhail Kabenyuk

In a finite group, a subset is called a Lagrange subset if its size divides the group order, and a factor if it admits a complementary subset. We provide a new and comparatively di…

math.GR2024

Factorizations of simple groups of order 168 and 360

Mikhail Kabenyuk

A finite group $G$ is called $k$ -factorizable if for any factorization $∣ G ∣ = a_{1} \dots a_{k}$ with $a_{i} > 1$ there exist subsets $A_{i}$ of $G$ with $∣ A_{i} ∣ = a_{i}$ such that $G=A_1\cdots A_k…

math.GR2023

Complete factorizations of finite groups

Mikhail Kabenyuk

Let $G$ be a group. The subsets $A_{1}, \dots, A_{k}$ of $G$ form a complete factorization of group $G$ if if they are pairwise disjoint and each element $g \in G$ is uniquely represente…