LAUSR

Abstract We consider pro-p-extensions of a number field in which the ramification and decomposition are restricted over an intermediate 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.