The distribution of second \(p\)-class groups on coclass graphs

DOI10.5802/jtnb.842zbMath1292.11126arXiv1403.3833OpenAlexW2962724215WikidataQ60546491 ScholiaQ60546491MaRDI QIDQ394270

Daniel C. Mayer

Publication date: 24 January 2014

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.3833

zbMATH Keywords

quadratic fieldcubic field\(p\)-class field tower\(p\)-class groupcoclass graphdihedral fieldsmetabelian \(p\)-groupprincipalization of \(p\)-classes

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class field theory (11R37) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Finite nilpotent groups, (p)-groups (20D15) Other abelian and metabelian extensions (11R20)

Related Items (5)

5-class towers of cyclic quartic fields arising from quintic reflection ⋮ 3-class field towers of exact length 3 ⋮ Annihilator ideals of two-generated metabelian p-groups ⋮ Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields ${\mathbb Q}(\sqrt{p_1p_2q}, \sqrt{-1})$ ⋮ Principalization algorithm via class group structure

Uses Software

• GAP
• Magma
• ANUPQ
• SmallGroups Library
• SymbCompCC

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