有限环上典型群的阶(英文)

Orders of Classical Groups over Finite Rings

英文关键词:Finite ring  Nilpotent radical  Classifical group  Free module.

中文摘要:

      本文通过“取模”，“取值和”，“取积”等方法，将有单位元的有限环Ｒ上典型群阶的计算转化为有限域上典型群阶的计算，并计算了Ｒ上ｎ－维自由模Ｖ_ｎ（Ｒ）中ｋ－维自由子模的个数．

英文摘要:

      It is observed that a classical group over a finite ring R with identity can be reduced to that over finite fields after the procedures of taking “modulo the radical”, “direct sum” and “tensor products”. Basing on that fact, we calculate the orders of classical groups over R and the number of k-dimensional free submodules of an n-dimensional free module over R .