Lemma 2.2 Let G be a finite group and M a maximal subgroup of G. Suppose G is not q-nilpotent and M = PQ is a minimal non-p-nilpotent group, where Pe Syly(M) and Q Syl (G). Then (1) Every proper subgroup of Q is normal in G. (2) IF M is not normal in G, then every proper subgroup of Q is contained in ZG)