c-正规子群与弱c-正规子群之间的关系(英文)

The Relation between c-normal Subgroups and Weakly c-normal Subgroups

群G的一个子群H称为在G中c-正规的,若存在G的一个正规子群K,使得G=HK并且H∩K≤HG,其中HG=∩g∈GHg是包含在H中的G的最大正规子群,群G的一个子群H称为在G中是弱c-正规的,若存在G的一个次正规子群K,使得G=HK并且H∩K≤HG.显然c-正规子群一定是弱c-正规子群,但反之并不一定成立.我们给出了c-正规子群与弱c-正规子群等价的若干充分条件.

A group H of G is called c-normal in G if there exists a normal subgroup K of G such that G=HK and H∩K≤HG where HG=∩g∈GHg is the maximal normal subgroup of G that is contained in H.A subgroup H of G is called weakly c-normal in G if there exists a subnormal subgroup K of G such that G=HK and H∩K≤HG.It is easy to see from the definition that a c-normal subgroup must be weakly c-normality,but the converse don＇t hold.Some equivalent conditions between c-normality and weakly c-normality were obtained.