Abstract
We present here the solution of a problem of J.-J. Sansuc together with a natural generalization of it. This problem of Sansuc is, given a number fieldk, to find the smallest positive integerm for which there exists a finitely generated subgroup of rankm ofk x having a dense image in (R ⊗ Q k)x under the canonical embedding. This integer is the number of archimedean places ofk plus one.
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