关键词: 有限局部环R=Z/2\+kZ,  , 斜对称矩阵,  , 伪辛群

Abstract:

Let \$R=Z/2\+kZ\$, where \$k>1\$. By matrix method , the normal forms of skewsymmetric matrices over \$R\$ are determined. Let \$G\+m\-p(R,H)={P∈GL\-m(R)|PHP′=H}\$ be  pseudosymplectic group determined by matrice \$H\$, where \$H=[JB((][HL(2]0[]I\+\{(v)\}\=-I\+\{(v)\}[]0[HL)][JB))]Δ，Δ=[JB((][HL(2]\{2\}[TX-]\+\{k-1\}[]\{1\}[TX-]\=-\{1\}[TX-][]0[HL)][JB))]. \$ The author  computes the order of  \$|G\+m\-P(R,H)|.\$

Key words: Finite local rings \$Z/2\+kZ\$, Skewsymmetric matrix, Pseudosymplectic groups