TOPOLOGICAL DYNAMICS OF STABLE GROUPS

Assume G is a group definable in a model M of a stable theory T. We prove that the semigroup SG(M ) of complete G-types over M is an inverse limit of some semigroups type-definable in Meq. We prove that the maximal subgroups of SG(M) are inverse limits of some definable quotients of subgroups of G. We consider the powers of types in the semigroup SG(M) and prove that in a way every type in SG(M) is profinitely many steps away from a type in a subgroup of SG(M).