Some Sufficient and Necessary Conditions for Nilpotent Groups

摘要

In this paper, we first define a special subgroup (i.e quasi-c-normal subgoup )of a finite group G which is a generalization of normal subgroups. A subgroup H of a group G is said to be quasi-c-normal in G if these exists a normal subgroup K of G such that G : HK is a power of a prime and H?K < Hg- Then we obtain some sufficient and necessary conditions for finite nilpotent groups by means of the quasi-c-normality of some subgroups of a group G and some know results are hence generalized.