We consider pro-p-extensions of a number field in which the ramification and decomposition are restricted over an intermediate ${\mathbb{Z}}_p$-extension. For such a maximal pro-p-extension under a certain restriction condition, we obtain a Koch type presentation of the pro-p Galois group by generators and relations. As its applications, we also obtain an extension of triple cubic residue symbols, a new example of arithmetical mild pro-p group, and another proof of a criterion of finiteness of certain Iwasawa modules.

中文翻译：

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关于在中间 Zp 扩展上具有限制分支的数字域的 pro-p 扩展

我们考虑一个数域的pro- p扩展，其中的分支和分解被限制在一个中间${\mathbb{Z}}_{磷}$-延期。对于这种在一定限制条件下的最大pro- p-扩展，我们通过生成器和关系获得了prop- p Galois群的Koch型表示。作为其应用，我们也获得三重立方残留符号的扩展，算术轻度亲的一个新实例p基团，和某些岩泽模块的有限性的标准的另一个证据。