p-Fitting子群的CAP-嵌入子群  

On CAP-Embedded Subgroups of p-Fitting Subgroups

作　　者：郭鹏飞[1,2] 郭秀云[2] 

机构地区：[1]连云港师范高等专科学校数学系,江苏连云港222006 [2]上海大学数学系,上海200444

出　　处：《数学的实践与认识》2010年第24期207-212,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10771132);生态风险评价中数学模型的构建(2010065)

摘　　要：群G的子群H称为G的CAP-嵌入子群,如果对于|H|的每个素因子p,存在G的某个CAP-子群K,使得H的某个Sylow p-子群也是K的一个Sylowp-子群.本文通过假定G的p-Fitting子群F_p(G)的某个Sylow p-子群的每个极大子群是G的CAP-嵌入子群,得到一些新的结果.A subgroup H of a finite group G is said to be CAP-embedded subgroup of G if, for each prime p dividing the order of H,there exists a CAP-subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K.In this paper,some new results are obtained based on the assumption that every maximal subgroup of some Sylow p-subgroup of p-Fitting subgroup F_p（G） have the CAP-embedded property in the group G.

关 键 词：CAP-嵌入子群 极大子群 P-幂零群 超可解群 

分 类 号：O152.1[理学—数学]