Abstract
Let G be a finite group. A subgroup H of G is said to be S-permutable in G if it permutes with all Sylow subgroups of G. In this note we prove that if P, the Sylow p-subgroup of G (p > 2), has a subgroup D such that 1 < vertical bar D vertical bar < vertical bar P vertical bar and all subgroups H of P with vertical bar H vertical bar = vertical bar D oe are S-permutable in G, then G' is p-nilpotent.