THE SECOND p-CLASS GROUP OF A NUMBER FIELD

DOI10.1142/S179304211250025XzbMath1261.11070arXiv1403.3899OpenAlexW2049577569WikidataQ56689263 ScholiaQ56689263MaRDI QIDQ3225629

Daniel C. Mayer

Publication date: 22 March 2012

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.3899

zbMATH Keywords

quadratic fieldscommutator calculuscubic fieldsprincipalizationcentral seriesdihedral fieldscoclass graphsmetabelian \(p\)-groups\(p\)-class groups\(p\)-class fields

Mathematics Subject Classification ID

Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Finite nilpotent groups, (p)-groups (20D15) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Other abelian and metabelian extensions (11R20)

Related Items (7)

Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ The distribution of second \(p\)-class groups on coclass graphs ⋮ Transfers of metabelian \(p\)-groups ⋮ 3-class field towers of exact length 3 ⋮ Unconditional class group tabulation of imaginary quadratic fields to $\|\Delta \| < 2^{40}$ ⋮ The group Gal(k3(2)|k) for k = ℚ(−3,d) of type (3,3) ⋮ Principalization algorithm via class group structure

Cites Work

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• Topics in computational algebraic number theory
• On a special class of \(p\)-groups
• Space groups and groups of prime-power order. I
• Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
• Sur les théoremes du genre principal et des ideaux principaux
• On 3-groups of second maximal class
• On the classification of prime-power groups by coclass
• Capitulation in Class Field Extensions of Type (p, p)
• Classifying 2-groups by coclass
• Idealklassen und Einheiten in kubischen Körpern

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