Submission date: 15 December 2012.

Abstract:

Assume G is a group de nable in a model M of a stable theory T. We prove that the semigroup S_G(M) of complete G-types over M is an inverse limit of some semigroups type-definable in M^{eq}. We prove that the maximal subgroups of S_G(M) are inverse limits of some defiquotients of subgroups of G. We consider the powers of types in the semigroup S_G(M) and prove that in a way every type in S_G(M) is pro-finitely many steps away from a type in a subgroup of S_G(M).

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