Abstract: c-Supplement is generalized and weak c-supple ment is introduced. Let Gbe a finite group and H a subgroup ofG.H is called weakly c supplemented in G if there exists a subgroup K of Gsuch that G=HK is the maximal quasinormal subgroup of Gcontained in H. Kis called a weak csupplement of Hin G. It is shown that for the least prime divisor p of the order of a finite group G and for a Sylow psubgroup P of G, if every 2maximal subgroup of P is  csupplemented in G and if G is not involved with A4, then G  is pnilpotent.

Key words: finite group, weak c-supplement, p-nilpotence