Building on Bosca's method, we extend to tame ray class groups the results on capitulation of ideals of a number field by composition with abelian extensions of a subfield first studied by Gras. More precisely, for every extension of number fields $K/\mathit{k}$, where at least one infinite place splits completely, and every squarefree divisor $\mathfrak{m}$ of K, we prove that there exist infinitely many abelian extensions $F/\mathit{k}$ such that the ray class group mod $\mathfrak{m}$ of K capitulates in KF. As a consequence we generalize to tame ray class groups the results of Kurihara on triviality of class groups for maximal abelian pro-extensions of totally real number fields.

在 Bosca 方法的基础上，我们通过与 Gras 首次研究的子域的阿贝尔扩展组合，将数域的理想投降结果扩展到驯服射线类组。更准确地说，对于数字字段的每个扩展$钾/\mathit{克}$，其中至少有一个无限的地方完全分裂，并且每个平方自由除数 $\mathfrak{米}$的K，我们证明存在无限多个阿贝尔扩展$F/\mathit{克}$ 这样射线类组mod $\mathfrak{米}$的K在KF 中投降。因此，我们将 Kurihara 关于全实数域的最大阿贝尔亲扩展的类群的平凡性的结果推广到驯服射线类群。