C-正规子群的若干等价条件

Some Equivalent Conditions for c-normal Subgroups

c-正规子群和弱c-正规子群是有限群的两个重要的概念。子群的弱c-正规性要比子群的c-正规性弱,利用子群的c-正规性已得出了群的很多重要的性质。但目前对弱c-正规子群的研究还较少,通过c-正规子群与弱c-正规子群对有限群结构的影响,得出c-正规子群与弱c-正规子群等价的一些充分条件。

c-normal subgroups and weakly c-normal subgroups play an important role in finite groups. A c-normal subgroup of G must be a weakly c-normal subgroup, but the converse is not ture in general. Many important results about finite group have been abtained by use the c-normality of subgroups. But the weakly c-normal subgroups are not the case, through the impact of c-normal subgroups and weakly c-normal subgroups on the structure of finite groups , some sufficient conditions for a weakly c-normal subgroup to be c-normal were given.