2018
Том 70
№ 2

# Factorizations of Finite Groups into $r$-Soluble Subgroups with Given Embeddings

Abstract

Let $X$ be a subset of the set of positive integers. A subgroup $H$ of a group $G$ is called $X$-subnormal in $G$ if there exists a chain of subgroups $H = H_0 ⊆ H_1 ⊆ … ⊆ H_n = G$ such that $|H_i : H_{i-1}| ∈ X$ for all $i$. We study the solubility and $r$ -solubility of a finite group $G = AB$ with some restrictions imposed on the subgroups $A$ and $B$ and on the set $X$ .

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 10, pp 1603-1608.

Citation Example: Knyagina V. N., Tyutyanov V. N. Factorizations of Finite Groups into $r$-Soluble Subgroups with Given Embeddings // Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1431–1435.

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