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中文摘要：
该文主要利用CC-子群的存在性来刻画有限群。首先,从CC-子群的存在性推导了一部分已知阶群的结构;其次,推导了当次正规子群和正规子群为CC-子群时的有限群的简单结构,得到了以下主要结论：定理1（1）若｜G｜=pq,p,q为素数,若G无CC-子群,则G为交换群。（2）若｜G｜=p2qn,p,q为奇素数,若G的CC-子群个数为1,则G为q幂零群.定理2设G为有限可解群,若G的每个次正规子群均为CC-子群,则｜G｜=pq。定理3设G为有限可解群,若G的每个正规子群为CC-子群,那么｜G｜=pqn,G=〈a〉G＇,其中,〈a〉为p阶子群。
英文摘要：
In this paper,the existence of CC-subgroups is used to describe finite groups.First,the structure of some already-known finite groups is deduced;then,by deducing the simple structure of the finite groups when its subnormal subgroups and normal subgroups are CC-subgroups respectively,the following conclusions are derived： Theorem one（1） if ｜G｜=pq,p,q is prime number and G has no CC-subgroups,hence G is Abel.（2） if ｜G｜=p2qn,p,q is odd prime,and G has only one CC-subgroups and then G is a nilpotent.Theorem two： G is a finite solvable group and every subnormal group is CC-subgroups,p,q are prime then ｜G｜=pq.Theorem three： G is a finite solvable group and every normal subgroups of G are CC-subgroups,then ｜G｜=pqn,G=〈a〉G′,p,q are prime,〈a〉 is a subgroup of order p.
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