Some properties of schemes in groups theory and top couples

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