Let G be a finite group and H a subgroup of G. We say that H is an H- subgroup in G if N-G( H) boolean AND H <= H-g for all g is an element of G; H is called weakly H- subgroup in G if it has a normal subgroup K such that G = HK and H boolean AND K is an H-subgroup in G. In this paper, we present some sufficient conditions for a group to be p-nilpotent under the assumption that certain subgroups of fixed prime power orders are weakly H-subgroups in G. The main results improve and extend new and recent results in the literature.
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