An example of an infinite tamely ramified Hilbert tower

Abstract.

In this note, we apply a refinement of the theorem of Golod-Safarevic (see {[3]) to the problem of the tamely ramified Hilbert 2-tower of a number field. As example, we prove that the maximal 2-extension of ${\Bbb Q}(\sqrt {-3*13*61})$ unramified outside 13 is infinite.