【摘要】 讨论群的性质时总是先研究群的元素的特点.利用(1,n;C)群中元素在复双曲空间珚HnC边界上的不动点的个数,决定元素分类的定义与矩阵的秩,讨论(1,n;C)群中在复双曲空间珚HnC边界上有一个公共不动点的两个元素的交换子的情形,得到(1,n;C)中的两个椭圆元素恰好在珚HnC中只有一个公共不动点时,两椭圆元素的交换子是抛物元素等结论.更多还原

【Abstract】 The discussion of group property always starts by examining the features of group elements.The element categorization is defined and the rank of a matrix is determined based on the number of fixed points on the boundary of complex hyperbolic space HnC of (1,n;C) elements.This paper discusses the situation where both elements have exactly one common fixed point on the boundary of nC,and concludes that the commutator of the two parabolic elements of (1,n;C) is an elliptic element when there is only one common fixed point in HCn.更多还原