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

  • V. N. Knyagina
  • V. N. Tyutyanov


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 $X$ .
How to Cite
Knyagina, V. N., and V. N. Tyutyanov. “Factorizations of Finite Groups into $r$-Soluble Subgroups With Given Embeddings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 10, Oct. 2014, pp. 1431–1435, http://umj.imath.kiev.ua/index.php/umj/article/view/2235.
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