  Let G be a group, and H a G-group defined by an imbedding map $G\rightarrow
H$; in [12] we have defined a topology on a subset of normal subgroups of $H$,
the so-called prime ideals. In this work, we generalize this topology to other
classes of groups.
  We hope that such topologies define new effective tools to tackle well-known
problems in groups theory.
  We study properties of the topology defined in [12], for example we define
the notions of functor of points, dimension and outline a Galois theory.
