Gauss's Lemma and some related group theory.

G. Miller

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Pure fields of degree 9 with class number prime to 3

Colin D. Walter (1980)

Annales de l'institut Fourier

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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 $n$ .