关于Sylow p-子群循环的12pn阶群的构造

摘要

Let p be an odd prime and G be finite groups of order 12pn such that p ＞5.In this paper,we classify and determine the structure of G,i.e.,we show that:If 12 divides (p-1),then there are 16 nonisomorphic classes ; if 12 divides (p-5),then 10 nonisomorphic classes,if 12 divides (p-7),then 14 monisomorphic classes and if 12 divides (p-11) then 9 nonisomorphic classes.%设p为奇素数,且p＞5,对Sylow p-子群循环的12pn阶群进行了完全分类并获得了其全部构造:1)当p≡1 (mod 12)时,G恰有16个彼此不同构的类型；2)当p≡5 (mod12)时,G恰有10个彼此不同构的类型；3)当p≡7 (mod 12)时,G恰有14个彼此不同构的类型；4)当p≡11 (mod 12)时,G恰有9个彼此不同构的类型.