有限群的弱s-置换嵌入子群  

Weakly s-Permutably Embedded Subgroups of Finite Groups

作　　者：钟国[1] 杨立英[1] 韦华全[1,2] 马儇龙[1] 周洋[1] 

机构地区：[1]广西师范学院数学科学学院,广西南宁530023 [2]广西大学数学与信息科学学院,广西南宁530004

出　　处：《杭州师范大学学报（自然科学版）》2013年第1期65-69,共5页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(10961007;11161006);广西自然科学基金项目(0991101;0991102);广西教育厅科研基金项目(201012MS140);广西高校人才资助计划(5070)

摘　　要：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.

关 键 词：P-超可解群 弱s-置换嵌入 有限群 

分 类 号：O152[理学—数学]