A Note on Ideal Class Groups

DOI10.1017/S0027763000012046zbMath0139.28104MaRDI QIDQ5514705

Kenkichi Iwasawa

Publication date: 1966

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.nmj/1118801632

zbMATH Keywords

cyclotomic fieldideal class groupsnormal extensionKummer theoremSylow p subgroup

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18)

Related Items (17)

On the Galois module structure of ideal class groups ⋮ Unnamed Item ⋮ Galois action on class groups ⋮ A NOTE ON THE EQUIVALENCE OF THE PARITY OF CLASS NUMBERS AND THE SIGNATURE RANKS OF UNITS IN CYCLOTOMIC FIELDS ⋮ A note on class numbers ⋮ On the history of the study of ideal class groups ⋮ Hilbert-Speiser number fields for a prime \(p\) inside the \(p\)-cyclotomic field ⋮ On the Exponents of Ideal Class Groups of Cyclotomic Fields ⋮ On the Ideal Class Groups of Imaginary Abelian Fields with Small Conductor ⋮ Minus class groups of the fields of the 𝑙-th roots of unity ⋮ Hilbert-Speiser number fields and the complex conjugation ⋮ Stickelberger ideals of conductor \(p\) and their application ⋮ On the parity of the class number of an imaginary abelian field of conductor \(2^{a} p^{b}\) ⋮ On the 2-part of the class numbers of cyclotomic fields of prime power conductors ⋮ Classes of order 4 in the strict class group of number fields and remarks on unramified quadratic extensions of unit type ⋮ On the ideal class groups of some cyclotomic fields ⋮ Solution of the class number two problem for cyclotomic fields

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