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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
Posted:
May 1, 2006
MathSciNet review:
2219042
Full-text PDF Free Access
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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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 . American J. of Mathematics  :  ,  .
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- S. Brueggeman. Septic Number Fields Which are Ramified Only at One Small Prime. J. Symbolic Computation
 :  ,  . MR 1828702 (2002e:11145)
- 2.
- G. Butler and J. Mckay. The transitive groups of degree up to eleven. Comm. Algebra
 ,  . MR 0695893 (84f:20005)
- 3.
- F. Diaz y Diaz. Tables minorant la racine
 -ième du discriminant d'un corps de nombres de degré  . Publications Mathématiques d'Orsay  ,  .MR 0607864 (82i:12007)
- 4.
- F. Diaz y Diaz. Petits discriminants des corps de nombres totalement imaginaires de degré
 . J. Number Theory  :  ,  . MR 0871167 (88a:11115)
- 5.
- F. Diaz y Diaz, J. Martinet and M. Pohst. The minimum discriminant of totally real octic fields. J. Number Theory
 :  ,  . MR 1072461 (91g:11128)
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- Y. Eichenlaub. Problèmes effectifs de théorie de Galois en degré à . Thèse soutenue à l'université de Bordeaux , .
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- J. Jones and D. Roberts. Sextic number fields with discriminant
 . In Number Theory : Fifth Conference of the Canadian Number Theory Association, CRM Proceedings and Lecture Notes  :  . American Mathematical Society, 1999. MR 1684600 (2000b:11142)
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- J. Martinet. Petits discriminants des corps de nombres. In Number theory days,
 (Exeter,  ), volume  of London Math. Soc. Lecture Note Series, pages  , Cambridge Univ. Press, Cambridge,  . MR 0697261 (84g:12009)
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- PARI/GP, version , Bordeaux, , http://pari.math.u-bordeaux.fr/.
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- M. Pohst. On the computation of number fields of small discriminants including the mininum discriminants of sixth degree fields. J. Number Theory
 :  ,  MR 0644904 (83g:12009)
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- S. Selmane. Odlyzko-Poitou-Serre lower bounds for discriminants for number fields. Maghreb Math. Rev., Vol.
 , No  ,  . MR 1871537 (2002j:11132)
- 12.
- R. Thompson. On the possible forms of discriminants of algebraic fields . American J. of Mathematics : , .
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Additional Information
Lesseni Sylla
Affiliation:
Université Bordeaux 1, Laboratoire d’Algorithmique Arithmétique, 351, Cours de la Libération, 33405 Talence Cedex, France
Email:
Sylla.Lesseni@math.u-bordeaux1.fr
DOI:
http://dx.doi.org/10.1090/S0025-5718-06-01827-8
PII:
S 0025-5718(06)01827-8
Keywords:
Number field,
nonsolvable
Received by editor(s):
November 10, 2004
Received by editor(s) in revised form:
May 3, 2005
Posted:
May 1, 2006
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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