有限群的弱Π嵌入子群（英文）

On weakly Π-embedded subgroups of finite groups

令G是1个有限群,且H是G的1个子群.子群H称为在G中是弱Π嵌入的,如果存在G的1个子群对(T,S)使得|G:HT|是某个素数的方幂,且(H∩T)/H_G≤S/H_G,其中T是G的1个包含H_G的拟正规子群且S/H_G≤H/H_G是G/H_G的1个满足Π性质的子群.这里利用弱Π嵌入子群研究有限群的结构.特别地,得到了子群是超循环嵌入的新判断准则.

Let Gbe a finite group and H a subgroup of G.His called weakly Π-embedded in Gif there exists a subgroup pair(T,S),where Tis a quasinormal subgroup of Gcontaining H_Gand S/H_G≤H/H_Gsatisfies Π-property in G/H_G,such that|G:HT|is a power of a prime and(H∩T)/H_G≤S/H_G.Here weaklyΠ-embedded subgroups were used to explore the structure of finite groups.In particular,new criterions of hypercyclically embedded subgroups were obtained.