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The Ambiguous Class Group and the Genus Group of Certain Non-Normal Extensions

Colin D. Walter

Séminaire de théorie des nombres de Grenoble

Pure fields of degree 9 with class number prime to 3

Colin D. Walter — 1980

Annales de l'institut Fourier

The main theorem gives necessary conditions and sufficient conditions for $Q (\sqrt[9]{n})$ to have class number prime to 3. These conditions involve only the rational prime factorization of $n$ and congruences mod 27 of the prime factors of $n$ . They give necessary and sufficient conditions for most $n$ .

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