素数幂、双素数幂阶元的共轭类长的个数为4的有限群的结构  

Structure of Finite Groups with Four Conjugacy Class Sizes of Primary and Biprimary Elements

作　　者：邵长国[1] 蒋琴会 SHAO Changguo;JIANG Qinhui(School of Mathematical Sciences, University of Jinan, Jinan 250022, China.)

机构地区：[1]济南大学数学科学学院,济南250022

出　　处：《数学年刊（A辑）》2018年第1期1-6,共6页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11301218);山东省自然科学基金项目(No.ZR2014AM020)的资助

摘　　要：设群G为一个有限群.如果群G中素数幂、双素幂阶元的共轭类长的集合为{1,p^a,m,p^bm},那么群G是可解的,其中a>b为正整数,p为素数且与m互素.进一步,给出了群G/Z(G)的结构,这是对文"Chen R F,Zhao X H.A criterion for a group to have nilpotent p-complements[J].Monatsh Math,2016,179(2):221-225"中定理A主要结论的一个推广.Let G be a finite group. It is proved that G is solvable if the set of its conjugacy class sizes of primary and biprimary elements is {1,p^a,m,p^bm}, where a 〉b are two positive integers and p is a prime coprime to integer m. Moreover, the authors give a detailed structure description of G/Z（G）, which generalizes the main result of Theorem A in ＂Chen,R. F. and Zhao, X. H., Monatsh. Math., 2016, 179（2）：221-225＂.

关 键 词：有限群 素数幂 双素幂阶元 共轭类长 2-Frobenius群 

分 类 号：O152.1[理学—数学]