Sur les extensions de ℚ à groupe de Galois S₄ et S̃₄

Arnaud Jehanne

Acta Arithmetica (1995)

  • Volume: 69, Issue: 3, page 259-276
  • ISSN: 0065-1036

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Arnaud Jehanne. "Sur les extensions de ℚ à groupe de Galois S₄ et S̃₄." Acta Arithmetica 69.3 (1995): 259-276. <http://eudml.org/doc/206687>.

@article{ArnaudJehanne1995,
author = {Arnaud Jehanne},
journal = {Acta Arithmetica},
keywords = {tables of octic polynomials; symmetric group; explicit construction of extension fields; Galois group; embedding problem},
language = {fre},
number = {3},
pages = {259-276},
title = {Sur les extensions de ℚ à groupe de Galois S₄ et S̃₄},
url = {http://eudml.org/doc/206687},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Arnaud Jehanne
TI - Sur les extensions de ℚ à groupe de Galois S₄ et S̃₄
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 3
SP - 259
EP - 276
LA - fre
KW - tables of octic polynomials; symmetric group; explicit construction of extension fields; Galois group; embedding problem
UR - http://eudml.org/doc/206687
ER -

References

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  5. [Bu-Fo-Po] J. Buchmann, D. Ford and M. Pohst, Enumeration of quartic fields with small discriminant, Math. Comp. 61 (1993), 873-879. Zbl0788.11060
  6. [B-McK] G. Butler and J. McKay, The transitive groups of degree up to eleven, Comm. Algebra 11 (1983), 863-911. Zbl0518.20003
  7. [Cr] T. Crespo, Explicit construction of Ãₙ type fields, J. Algebra 127 (1989), 452-461. Zbl0704.11043
  8. [Gr] G. Gras, Sur les l-classes d'idéaux dans les extensions cycliques relatives de degré premier l, Ann. Inst. Fourier (Grenoble) 23 (3) (1973), 1-48. Zbl0276.12013
  9. [He] E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer, New York, 1981. 
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  11. [Ja] J.-F. Jaulent, L'arithmétique des l-extensions, Thèse, Publ. Math. Fac. Sci. Besançon, 1986. 
  12. [Ma] J. Martinet, Discriminants and permutation groups, dans: Number Theory, R. Mollin (éd.), Walter de Gruyter, Berlin, 1990, 359-385. 
  13. [M-P] J. Martinet et J.-J. Payan, Sur les extensions cubiques non galoisiennes des rationnels et leur clôture galoisienne, J. Reine Angew. Math. 228 (1967), 15-37. Zbl0161.05302
  14. [Sc] I. Schur, Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 139 (1911), 155-250. Zbl42.0154.02
  15. [Se1] J.-P. Serre, L'invariant de Witt de la forme Tr(x²), Comment. Math. Helv. 59 (1984), 651-676. 
  16. [Se2] J.-P. Serre, Corps locaux, 3e éd., Hermann, Paris, 1980. 
  17. [Se3] J.-P. Serre, Représentations linéaires des groupes finis, 3e éd., Hermann, Paris, 1978. Zbl0407.20003

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