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We define a sequence of rational integers $u_i\left(E\right)$ for each finite index subgroup E of the group of units in some finite Galois number fields K in which prime p ramifies. For two subgroups E’ ⊂ E of finite index in the group of units of K we prove the formula $v_p\left([E:E^{\text{'}}]\right)={\sum }_{i=1}^r{u}_i\left(E^{\text{'}}\right)-u_i\left(E\right)$. This is a generalization of results of P. Dénes [3], [4] and F. Kurihara [5].