New number fields with known p-class tower

Abstract

The p-class tower $F_p^{\infty }(k)$ of a number field k is its maximal unramified pro-p extension. It is considered to be known when the p-tower group, that is the Galois group $G:=Gal(F_p^{\infty }(k)/k)$, can be identified by an explicit presentation. The main intention of this article is to characterize assigned finite 3-groups uniquely by abelian quotient invariants of subgroups of finite index, and to provide evidence of actual realizations of these groups by 3-tower groups G of real quadratic fields $K=Q(\sqrt{d})$ with 3-capitulation type (0122) or (2034).

25 pages, 5 figures; presented at the 22nd Czech and Slovak International Conference on Number Theory in Liptovsky Jan, Slovakia, on August 31, 2015