p-Fitting子群的CAP-嵌入子群

On CAP-Embedded Subgroups of p-Fitting Subgroups

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.