Abstract
Let [Formula: see text] be a finite group and [Formula: see text] a subgroup of [Formula: see text]. [Formula: see text] is said to be [Formula: see text]-embedded in [Formula: see text] if there exists a normal subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] is a Hall subgroup of [Formula: see text] and [Formula: see text], where [Formula: see text] is the largest [Formula: see text]-semipermutable subgroup of [Formula: see text] contained in [Formula: see text]. In this paper, we give some new characterizations of [Formula: see text]-nilpotent and supersolvable groups by using [Formula: see text]-embedded subgroups. Some known results are generalized.
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