有限群的弱s-置换嵌入子群

Weakly s-Permutably Embedded Subgroups of Finite Groups

群G的一个子群H称为在G中s-置换嵌入,如果对于任意的素数p||H|,H的Sylowp-子群也是G的某个s-置换子群的Sylowp p-子群.称群G的子群H在G中弱s-置换嵌入,如果存在群G的次正规子群T和包含在H中的G的一个s-置换嵌入子群Hse,使得G=HT且H∩T≤Hse.利用弱s-置换嵌入子群的概念,研究了超可解群的构造,获得了有限群为p-超可解的一些充分条件.

A subgroup H of a finite group G is called s-permutably embedded in G if for each prime P｜｜ H｜, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutably subgroup of G. A subgroup H of a group G is said to be weakly s-permutably embedded in G if there is a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G is contained in H, such that G= HT and H∩ T≤Hse. Using this concept, the paper investigated the structure of p- supersolvable groups and obtained some sufficient conditions of p-supersolvability on finite groups.