On the growth of \(p\)-class groups in \(p\)-class field towers

DOI10.1006/jabr.1996.6849zbMath0879.11069OpenAlexW2050121250MaRDI QIDQ1355512

Farshid Hajir

Publication date: 18 January 1998

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1996.6849

zbMATH Keywords

\(p\)-class field towers\(p\)-class groupsHilbert \(p\)-class field

Mathematics Subject Classification ID

Class field theory (11R37) Class field theory; (p)-adic formal groups (11S31)

Related Items

SELMER GROUPS AND GENERALIZED CLASS FIELD TOWERS ⋮ The growth of fine Selmer groups ⋮ GOLOD–SHAFAREVICH GROUPS: A SURVEY ⋮ A remark on Boston's question concerning the existence of unramified \(p\)-extensions. II ⋮ Counting isospectral manifolds ⋮ Unnamed Item ⋮ Heuristics and conjectures in the direction of a $p$-adic Brauer–Siegel Theorem ⋮ On the Fontaine-Mazur conjecture for number fields and an analogue for function fields ⋮ Some problems on \(p\)-class field towers ⋮ Counting maximal arithmetic subgroups. Appendix by Jordan Ellenberg and Akshay Venkatesh ⋮ Growth of Fine Selmer Groups in Infinite Towers ⋮ Corrigendum The number of generators of finite p-groups ⋮ On the locally cyclotomic tower of a number field ⋮ INFINITE HILBERT CLASS FIELD TOWERS OVER CYCLOTOMIC FIELDS ⋮ Some cases of the Fontaine-Mazur conjecture. II ⋮ Unramified subextensions of ray class towers

Cites Work

• Unnamed Item
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• Powerful \(p\)-groups. II: \(p\)-adic analytic groups
• A note on the group of units of an algebraic number field
• Group presentation, p-adic analytic groups and lattices in \(SL_ 2({\mathbb{C}})\)
• A group theoretic characterization of linear groups
• Combinatorial group theory for pro-p groups
• Identities for Lie algebras of pro-\(p\) groups
• Some cases of the Fontaine-Mazur conjecture
• Class numbers and \(\mathbb Z_p\)-extensions
• Tours de corps de classes et estimations de discriminants
• On some \(\Lambda\)-analytic pro-\(p\) groups
• On a theorem of Koch
• Finite presentations of pro-\(p\) groups and discrete groups
• \(p\)-adic analytic groups
• Free subgroups in linear groups
• Norme relative de l'unité fondamentale et 2-rang du groupe des classes d'idéaux de certains corps biquadratiques
• Relative Genus Theory and the Class Group of l-Extensions
• On the maximal unramified p-extension of an algebraic number field.
• Zum Satz von GOLOD‐SCHAFAREWITSCH