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For a rational prime $p\neq 2$, we compute the sequence of ramificationgroups of a Galois, radical and finite extension $L/F$ where $F/\mathbb{Q}_p$is an unramified finite extension. First, we compute it in the case where theexponent of Gal$(L/F)$ is a power of $p$, by a Hecke's theorem and someinductions,. Finally, we deal with the general case. For the case $p=2$, thesame method can work, provided that we make an additional hypothesis.

Calcul des groupes de ramification de certaines extensions radicales