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

• Date: 2014
• Main Authors: Knyagina, V. N., Tyutyanov, V. N., Княгина, В. Н., Тютянов, В. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2235
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $G = AB$ wit...