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Let us consider a linear control system \Sigma on a connected Lie group G. Itis known that the accessibility set A from the identity e is in general not asemigroup. In this article we associate a new algebraic object S to \Sigmawhich turns out to be a semigroup, allowing the use of the semigroup machineryto approach \Sigma. In particular, we obtain some controllability results.

A Semigroup associated to a linear control system on a Lie group