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Version définitive.International audienceThis work falls within the theory of linear forms in logarithms over a connected and commutative algebraic group, defined over the field of algebraic numbers $\overline{Q}$. Let $G$ be such a group. Let $W$ be a hyperplane of the tangent space at the origin of $G$, defined over $\overline{Q}$, and $u$ be a complex point of this tangent space, such that the image of $u$ by the exponential map of the Lie group $G(C)$ is an algebraic point. Then we obtain a lower bound for the distance between $u$ and $W\otimes\mathbf{C}$, which improves the results known before and which is, in particular, the best possible for the height of the hyperplane $W$. The proof rests on Baker's method and Hirata's reduction as well as a new arithmetic argument (Chudnovsky's process of variable change) which enables us to give a precise estimate of the ultrametric norms of some algebraic numbers built during the proof

Mesures d’indépendance linéaire de logarithmes dans un groupe algébrique commutatif