Mathematische Nachrichten

Application of Greenberg's conjecture in the capitulation problem

Early View

Abstract

Let r be a positive integer. Assume Greenberg's conjecture for some totally real number fields, we show that there exists an infinite family of imaginary cyclic number fields F over the field of rational number field Q , with an elementary 2‐class group of rank equal to r that capitulates in an unramified quadratic extension over F. Also, we give necessary and sufficient conditions for the Galois group of the unramified maximal 2‐extension over F to be abelian.

Related Topics

Related Publications

Related Content

Site Footer

Biostatistics

Topics:

Business & Economics

Topics:

Engineering

Topics:

Environmental

Topics:

Methods

Topics:

Social Sciences

Topics:

Tools

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.