| Two elements in a group G are in the same z-class if their centralizers are conjugate to each other. The z-classes turn out to be internal ingredients of a group which determines the "dynamics" of G when it
acts on a set X. It is an interesting problem to parametrize the conjugacy and z-classes in a group. In this talk, we shall describe this parametrization for the isometries of the hyperbolic space, and discuss some progress for the isometries of a quadratic space over a field of characteristic not two. |