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