An example of an infinite tamely ramified Hilbert tower

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ {\Bbb Q}(\sqrt {-3*13*61}) $\end{document} unramified outside 13 is infinite.