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).
出处
《武汉大学学报（理学版）》
CAS
CSCD
北大核心
2005年第S2期37-39,共3页
Journal of Wuhan University:Natural Science Edition
关键词
超可解群
扩张
同余
循环群
supersolvable group
extension
congruent
cyclic group
