New number fields with known p-class tower

Mayer, Daniel C.

doi:10.1515/tmmp-2015-0040

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).

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New number fields with known p-class tower

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