c-正规子群对有限群构造的影响

The Influence of c-normal subgroups on the Structure of Finite Groups

设群G为有限群,称G的子群H在G中c 正规,如果存在G的一个正规子群K,使得G=HK且H∩K≤HG,其中HG是包含在H中的G的最大正规子群.本文运用子群的c 正规性刻画了有限群的结构,由此获得了一些新的结论,并且推广了关于p 幂零群、亚幂零群的一些已知结果.

Let G a finite group. We called a subgroup H of a group G c-normal if there exists a normal subgroup K of G such that G=KH and H∩K≤H_G, where H_G is the largest normal subgroup of G contained in H. By using the normality of subgroups, we shall determine the structure of some finite groups. Some new results are obtained and some known results of p-nilpotnet groups and metanilpotent groups are generalized.