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

Abstract

Let σ = {πi|i ∈ I and πi ∩ πj = ∅ for all i 6= 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 πi-maximal subgroups for all πi ∈ 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.