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

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.

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.

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Publié le :
DOI : https://doi.org/10.5802/jtnb.562
Mots clés : Nonic field. Galois group. Nonsolvable
@article{JTNB_2006__18_3_617_0,
     author = {Sylla Lesseni},
     title = {Nonsolvable nonic number fields ramified only at one small prime},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {617--625},
     publisher = {Universit\'e Bordeaux 1},
     volume = {18},
     number = {3},
     year = {2006},
     doi = {10.5802/jtnb.562},
     zbl = {pre05186995},
     mrnumber = {2330431},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.562/}
}
Sylla Lesseni. Nonsolvable nonic number fields ramified only at one small prime. Journal de Théorie des Nombres de Bordeaux, Tome 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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