On NH-embedded subgroups of finite groups.

Let G be a finite group and H a subgroup of G. H is said to be N H -embedded in G if there exists a normal subgroup T of G such that H T is a Hall subgroup of G and H ∩ T ≤ H s ̄ G , where H s ̄ G 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 N H -embedded subgroups. Some known results are generalized. [ABSTRACT FROM AUTHOR]