Abstract
Let G be a classical group, X be the semisimple element in G and G(k) be the k-rational points of G, we want to discuss the behavior of centralizers of a semisimple element in classical groups. For G = GL(V) where V is a vector space of dimension n, we can explicity describe the centralizer of a semisimple element. When G is orthogonal, sympletic, unitary groups of V, let A(X) be the k-algebra generated by X and V (X) = V as A-module, we can define a sesquilinear form F(X) : V (X) × V (X) → A(X) such that it is the subgroup of invertible linear transformations of V preserving F(X).