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The nonexistence of nonsolvable octic number fields ramified only at one small prime

Author: Lesseni Sylla
Journal: Math. Comp. 75 (2006), 1519-1526
MSC (2000): Primary 11Y40; Secondary 11R21
Published electronically: May 1, 2006
MathSciNet review: 2219042
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Abstract: We prove that there is no primitive octic number field ramified only at one small prime, and so no such number field with a nonsolvable Galois group.

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Lesseni Sylla
Affiliation: Université Bordeaux 1, Laboratoire d’Algorithmique Arithmétique, 351, Cours de la Libération, 33405 Talence Cedex, France

Keywords: Number field, nonsolvable
Received by editor(s): November 10, 2004
Received by editor(s) in revised form: May 3, 2005
Published electronically: May 1, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.