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Let G be a finite group. Suppose that H is a subgroup of G. We say that H is s-semipermutable in G if HGp=GpH for any Sylow p-subgroup Gpof G with (p,|H|)=1,where p is a prime dividing the order of G. We give a p-nilpotent criterion of G under the hypotheses that some subgroups of G are s-semipermutable in G. Our result is a generalization of the famous Burnside’s p-nilpotent criterion.