Mobius变换中的n阶循环群判别式  

n-order cycle group criterion of Mobius transformation

作　　者：甘欣荣[1] 江乐[1] 钟寿国[2] 

机构地区：[1]武汉科技大学理学院,武汉430065 [2]武汉大学数学与统计学院,武汉430072

出　　处：《黑龙江大学自然科学学报》2016年第2期170-174,共5页Journal of Natural Science of Heilongjiang University

基　　金：湖北省教育厅科研计划重点项目(D20111110)

摘　　要：M?bius变换的n阶循环群生成元的充要条件表达式中,含有一系列Δ_m(齐次多项式,1≤m≤n)。而随着n的增大,Δ_n的次数增高,条件也增多。为解决此问题,用清除Δ_n中关于n低下标因子的方法,使其在整系数域内,用互质的判别式{Δ*_n}等价地取代{Δ_n},从而尽可能地降低Δ_n的次数,同时使判据简洁地成为一个条件。The expression of necessary and sufficient condition of n-order cycle group generating element for Mfibius transformation contains a series of Am （ homogeneous multinomial, 1 ≤m≤ n）. With the increasing of n, both the order of △n and the conditions increase. To solve this problem, the method of clearing away low index factor related to n in An is employed. Thereby, relatively-prime criterion { △n＊ / is equivalently used to replace {△n} in the integer coefficient field. In this way, not only the order of △n is reduced, but also the criterion becomes a condition compactly.

关 键 词：MOBIUS变换 互质多项式 整系数域 判别式 

分 类 号：O152.1[理学—数学] O152.3[理学—基础数学]