有限群可解的若干充分条件

Some Sufficient Conditions for Solvability of Finite Groups

群G的一个子群H称为在G中弱c-正规,若存在G的一个次正规子群K使得G=HK且H∩K≤HG,其中HG=∩g∈GHg是包含在H中G的最大的正规子群.弱c-正规子群是近年来群论研究的热点.利用子群的弱c-正规性对有限群的影响,得到了关于有限群可解的若干充分条件.

A subgroup H of a finite group G is said to be weakly c-normal in G if there exists a subnormal subgroup K of G such that G = HK and H∩K≤ HG, where HG is the maximal normal subgroup of G that is contained in H. The researchon weakly c-normal subgroups has been Proposed by many Scholars for a long time, and the research in this field is still very active. Using weakly c-normal subgroups, some sufficient conditions for solvability of finite groups are obstained.