In this paper, we investigate the influence of Ssemipermutable and weakly S-supplemented subgroups on the pnilpotency of finite groups. Some recent results are generalized. Keywords—S-semipermutable, weakly S-supplemented, pnilpotent.

The O’Nan-Scott theorem weakly classifies the maximal subgroups of the symmetric group S, providing some information about the lattice Λ of subgroups of S. We wish to obtain more information about Λ. We proceed by determining the intersection H of suitable pairs of maximal subgroups of S and the sublattice of overgroups of H in S.