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Abstract

We define a sequence of rational integers $u_i(E)$ 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 $v_p([E:E']) = ∑_{i=1}^r {u_i(E') - u_i(E)}$. This is a generalization of results of P. Dénes [3], [4] and F. Kurihara [5].