Cyclotomic Swan subgroups and irregular indices

DOI10.1216/RMJM/1020171578zbMath0991.11059OpenAlexW2071180044MaRDI QIDQ5948870

Daniel R. Replogle

Publication date: 12 November 2001

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol31-2/CONT31-2/CONT31-2.html

zbMATH Keywords

index of irregularitygroup ringlocally free class group

Mathematics Subject Classification ID

Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (5)

Nontrivial Galois module structure of cyclotomic fields ⋮ Cyclotomic Swan subgroups and primitive roots. ⋮ Sequences of Hopf-Swan subgroups. ⋮ Computation of several cyclotomic Swan subgroups ⋮ On the self-duality of rings of integers in tame and abelian extensions

Cites Work

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• Nontrivial lower bounds for class groups of integral group rings
• A note on Swan modules
• Swan modules and realisable classes for Kummer extensions of prime degree
• Relative Galois module structure of quadratic extensions
• Galois module structure of elementary abelian extensions
• A Mayer-Vietoris sequence for class groups
• Kernel groups and nontrivial Galois module structure of imaginary quadratic fields
• Swan modules and Hilbert-Speiser number fields
• Computation of several cyclotomic Swan subgroups
• Galois module structure of abelian extensions.

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