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 ramifié en un unique premier petit. Il n’existe donc pas de corps de nombres de degré ramifié en un unique premier petit et ayant un groupe de Galois non résoluble.
@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},
mrnumber = {2330431},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.562/}
}
TY - JOUR AU - Sylla Lesseni TI - Nonsolvable nonic number fields ramified only at one small prime JO - Journal de théorie des nombres de Bordeaux PY - 2006 SP - 617 EP - 625 VL - 18 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.562/ DO - 10.5802/jtnb.562 LA - en ID - JTNB_2006__18_3_617_0 ER -
%0 Journal Article %A Sylla Lesseni %T Nonsolvable nonic number fields ramified only at one small prime %J Journal de théorie des nombres de Bordeaux %D 2006 %P 617-625 %V 18 %N 3 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.562/ %R 10.5802/jtnb.562 %G en %F JTNB_2006__18_3_617_0
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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