关于只有有限个子群不满足幂条件的有限群  

On Finite Groups with Many Finitely Subgroups Not Satisfying the Exponent Condition

作　　者：吕恒[1] 段泽勇[1] 余大鹏[2] 

机构地区：[1]西南师范大学数学与财经学院,重庆400715 [2]渝西学院数学系,重庆402168

出　　处：《西南师范大学学报（自然科学版）》2003年第5期746-749,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10171074);教育部科学技术重点项目.

摘　　要：证明了一个有限群G如果只有4个子群满足幂条件,那么G≌Z3×Z3.同时还证明了一个有限群G如果只有5个子群不满足幂条件,那么群G≌Z2×Z4或G≌D8或G≌Gk,Gk=〈a,b｜a5=b2n=1,b-1ab=ak,k=2,3,4,b2a=ab2〉.In this paper, we have proved that if a finite group G with 4 subgroups not satisfying exponent condition, then G≌Z_3×Z_3 or G≌Z_2×Z_4, meanwhile, we also proved that: if a finite group G with 5 subgroups not satisfying exponent condition, then G≌Z_2×Z_4 or G≌D_8 or G≌G_k, G_k=<a, b|a^5=b^(2^n)=1, b^(-1)ab=a^k, k=2,3,4, b^2a=ab^2>.

关 键 词：有限群 DEDEKIND群 次正规子群 超可解群 幂子群 幂条件 

分 类 号：O152.1[理学—数学]