Nonsolvable nonic number fields ramified only at one small prime
Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 3, pp. 617-625.

We prove that there is no primitive nonic number field ramified only at one small prime. So there is no nonic number field ramified only at one small prime and with a nonsolvable Galois group.

On montre qu’il n’existe pas de corps de nombres primitif de degré 9 ramifié en un unique premier petit. Il n’existe donc pas de corps de nombres de degré 9 ramifié en un unique premier petit et ayant un groupe de Galois non résoluble.

DOI: 10.5802/jtnb.562
Keywords: Nonic field. Galois group. Nonsolvable
Sylla Lesseni 1

1 Université Bordeaux 1 Laboratoire d’Algorithmique Arithmétique 351, Cours de la Libération 33405 Talence Cedex, France.
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Sylla Lesseni. Nonsolvable nonic number fields ramified only at one small prime. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 3, pp. 617-625. doi : 10.5802/jtnb.562. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.562/

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