Finite groups with some \(S \)-permutably embedded subgroups (Q6133124)

A subgroup \(H\) of a finite group \(G\) is \(S\)-permutably embedded in \(G\) if each Sylow subgroup of \(H\) is a Sylow subgroup of some \(S\)-permutable subgroup of \(G\). The authors investigate the structure of the finite groups some of whose subgroups are \(S\)-permutably embedded. Their results improve and generalize many available results.