一类4pq(p>q≠3)阶群的构造  

Structure of Some Groups of Order of 4pq(p>q≠3)

作　　者：古鲁峰[1] 黄若静[1] 张林兰[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2005年第S2期37-39,共3页Journal of Wuhan University:Natural Science Edition

摘　　要：在有限群理论中,确定n阶群的构造是一个分类问题.利用了超可解群的性质,通过群的扩张理论解决了在p 1(modq)时4pq(p>q≠3)群的构造,即证明了下面的定理:当p/≡1(modq)时4pq(p>q>3)阶群的构造:①10种,p/≡1(mod 4),q/≡1(mod 4)时;②16种,p≡1(mod 4),q≡1(mod 4)时.③12种,p≡1(mod 4),q/≡1(mod 4)时;④12种,p/≡1(mod 4),q≡1(mod 4)时.The paper tries to solve the structure of some groups of order of 4pq(p,q,are odd numbers and p>q>3),using some properties in supersolvable groups and some theorems in extension of groups we obtain the following theorem: When p((≡))1(modq),then① G has 10 types,when p((≡))1(mod 4),q((≡))1(mod 4);② G has 16 types,when p≡1(mod 4),q≡1(mod 4);③ G has 12 types,when p≡1(mod 4),q((≡))1(mod 4);④ G has 12 types,when p((≡))1(mod 4),q≡1(mod 4).

关 键 词：超可解群 扩张 同余 循环群 

分 类 号：O152.1[理学—数学]