Let G be a finite group and H a subgroup of G. H is said to be NH-embedded in G if there exists a normal subgroup T of G such that HT is a Hall subgroup of G and H∩T≤Hs̄G, where Hs̄G is the largest s-semipermutable subgroup of G contained in H. In this paper, we give some new characterizations of p-nilpotent and supersolvable groups by using NH-embedded subgroups. Some known results are generalized.
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