Abstract:

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.

Key words: Unitary group, Order, Local ring