<abstract xmlns="http://www.w3.org/1999/xhtml"> 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). </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).

New number fields with known p-class tower

Tatra Mountains Mathematical Publications

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{"article-title":"New number fields with known p-class tower"}

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...

New number fields with known p-class tower

Published Online: Feb 19, 2016

Page range: 21 - 57

Received: Nov 02, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0040

Keywords
p-class field towers, p-capitulation, p-class groups, quadratic fields, cubic fields, dihedral fields, finite p-groups, descendant trees, p-group generation algorithm

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

New number fields with known p-class tower

Published Online: Feb 19, 2016

Page range: 21 - 57

Received: Nov 02, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0040

Keywordsp-class field towers, p-capitulation, p-class groups, quadratic fields, cubic fields, dihedral fields, finite p-groups, descendant trees, p-group generation algorithm

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
p-class field towers, p-capitulation, p-class groups, quadratic fields, cubic fields, dihedral fields, finite p-groups, descendant trees, p-group generation algorithm