有限交换环上CHEVALLEY群的阶

ORDERS OF CHEVALLEY GROUPS OVER FINITE COMMUTATIVE RINGS

设Ｒ是一个含单位元的有限交换环，Ｇ是由一个连通复单李群及其一个忠实表示确定的Ｃｈｅｖａｌｌｒｙ－Ｄｅｍａｚｕｒｅ群概形，Ｇ（Ｒ）是环Ｒ上的Ｃｈｅｖａｌｌｅｙ群，本文的目的是计算有限群Ｇ（Ｒ）的阶．

Let R be an arbitrary finite commutative ring with identity. Denote by G a Cheyal ley-Demazure group scheme associated with a connected complex simple Lie grasp Gc and a faithfull representation of Gc. Let G(R) be a Chevalley group over the ring R. The aim of this paper is to calculate the order of the finite group G(R)