有限局部环上酉群阶的计算

设K=F_(q^2),其特征为p, q=p^α,K有对合自同构ω:a→a^q. G是一个p 群，其阶为p^β, 群代数R=KG为一局部环. K的2阶自同构ω可延拓为R的一个2阶自同构，记为ω'，为方便，对任意a∈R, 记ω‘(a)为~a. R上2n级酉群定义为U_(2n)R={A∈GL_(2n)R|A(0,I^n,I^n,0)~A^t=(0,I^n,I^n,0)} 该文计算了U_(2n)R的阶. 

Computation of the Orders of Unitary Groups Over Finite Local |Rings

Assume that K=F_(q^2),where q=p^α, Let  G be a p-group of order p^β and R=KG. Define an  involutive automorphism of K by ω:a→a^q.Denote by ω′ the involutive automorphism extended from K to R. For any a∈R, write ~a=ω′(a). Define unitary groups of degree 2n over R by U_(2n)R={A∈GL_(2n)R|A(0,I^n,I^n,0)~A^t=(0,I^n,I^n,0)} .In this paper, the author  computes the order of  U_(2n)R.