Submission date: 8 July 2013.

Abstract:

Given a subroup G of a stable (in the model-theoric sense) group Γ, we establish some properties of the traces on G of the definable subsets of Γ. We give a special attention to the case when Γ is a group of finite Morley rank. An example of this situation is provided by the linear groups : for some n, G is a subgroup of GL_n(K), where K is a field that we may take algebraically closed ; the definable sets in the sense of GL_n(K) are its constructible subsets, i.e. the boolean combinations of a finite number of its Zariski closed subsets.

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