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Let A be a complex abelian variety and G its Mumford-Tate group. Supposing that the simple abelian subvarieties of A are pairwise non-isogenous, we find a lower bound for the rank rk G of G, which is a little less than log 2 dim A. If we suppose that End A is commutative, then we show that rk G ≥ log 2 dim A + 2, and this latter bound is sharp. We also obtain the same results for the rank of the ℓ-adic monodromy group of an abelian variety defined over a number field. Résumé (Minoration desdoi:10.24033/bsmf.2684 fatcat:vfswbuukhzhbtoh6sc33jlokae