New number fields with known p-class tower

2015/10/02 by Mayer, Daniel C.
#11R11 #11R16 #11R20 #11R29 #11R37 #20-04 #20D15 #20F05 #20F12 #20F14 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1510.00565

Abstract

The p-class tower F_p^∞(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^∞(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(√(d)) with 3-capitulation type (0122) or (2034).

Related

• Recent progress in determining p-class field towers
• Criteria for three-stage towers of p-class fields
• Heuristics for p-class towers of real quadratic fields
• Successive approximation of p-class towers
• Computation of Galois groups associated to the 2-class towers of some quadratic fields