On a generalization of the concept of S-permutable subgroup of a finite group

V. I. Murashka

paper

On a generalization of the concept of S-permutable subgroup of a finite group

arXiv:1610.03006

Abstract

Let $σ = {π_{i} ∣ i \in I$ and $π_{i} \cap π_{j} = \emptyset$ for all $i \neq = j}$ be a partition of the set of all primes into mutually disjoint subsets. In this paper we considered subgroups that permutes with given sets of $π_{i}$ -maximal subgroups for all $π_{i} \in σ$ . In particular we showed that such subgroups forms a sublattice of the lattice of all subgroups of a finite group. As corollaries we obtained some well known results about $S$ -permutable subgroups.