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Let G be a finite group. For a finite p-group P the subgroup generated by all elements of order p is denoted by Ω1(p). Zhang [5] proved that if P is a Sylow p-subgroup of G, Ω1(P) ≦ Z(P) and N G(Z(P)) has a normal p-complement, then G has a normal p-complement. The object of this paper is to generalize this result.

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