Sur les extensions de groupe de Galois Ã₄

C. Bachoc; S.-H. Kwon

Acta Arithmetica (1992)

  • Volume: 62, Issue: 1, page 1-10
  • ISSN: 0065-1036

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C. Bachoc, and S.-H. Kwon. "Sur les extensions de groupe de Galois Ã₄." Acta Arithmetica 62.1 (1992): 1-10. <http://eudml.org/doc/206477>.

@article{C1992,
author = {C. Bachoc, S.-H. Kwon},
journal = {Acta Arithmetica},
keywords = {alternating group; Galois embedding problem; Galois extensions; Galois group; octic fields; octic polynomials},
language = {fre},
number = {1},
pages = {1-10},
title = {Sur les extensions de groupe de Galois Ã₄},
url = {http://eudml.org/doc/206477},
volume = {62},
year = {1992},
}

TY - JOUR
AU - C. Bachoc
AU - S.-H. Kwon
TI - Sur les extensions de groupe de Galois Ã₄
JO - Acta Arithmetica
PY - 1992
VL - 62
IS - 1
SP - 1
EP - 10
LA - fre
KW - alternating group; Galois embedding problem; Galois extensions; Galois group; octic fields; octic polynomials
UR - http://eudml.org/doc/206477
ER -

References

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  1. [B] S. Böge, Witt-Invariante und ein gewisses Einbettungsproblem, J. Reine Angew. Math. 410 (1990), 153-159. 
  2. [BPS] J. Buchman, M. Pohst and J. v. Schmettow, On the computation of unit groups and class groups of totally real quartic fields, Math. Comp. 52 (185) (1989), 161-174. 
  3. G. Butler and J. McKay, The transitive groups of degree up to eleven, Comm. Algebra 11 (8) (1983), 863-911 . Zbl0518.20003
  4. [C1] T. Crespo, Explicit construction of Ãₙ type fields, J. Algebra 127 (1989), 452-461. Zbl0704.11043
  5. [C2] T. Crespo, Embedding problems with ramification conditions, J. Number Theory, to appear. Zbl0648.12007
  6. [H-K] F.-P. Heider and P. Kolvenbach, The construction of Sl(2,3)-polynomials, J. Number Theory 19 (1984), 392-411. Zbl0566.12003
  7. [K] P. Kolvenbach, Zur algebraischen und arithmetischen Theorie der Sl(2,3)- Erweiterungen, Dissertation, Köln 1982. 
  8. [K1] S.-H. Kwon, Extensions à groupe de Galois A₄, Thèse, Univ. Bordeaux I, 1984. 
  9. [K2] S.-H. Kwon, Corps de nombres de degré 4 de type alterné, C. R. Acad. Sci. Paris 299 (2) (1984), 41-43. Zbl0564.12007
  10. [M] J. Martinet, Discriminants and permutation groups, dans : Number Theory, R. Mollin (éd.), Walter de Gruyter, Berlin 1990, 359-385. 
  11. [Sc] I. Schur, Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, J. Crelle 139 (1911), 155-250 (= Ges. Abh. I, 346-441). Zbl42.0154.02
  12. [S1] J.-P. Serre, L'invariant de Witt de la forme Tr(x²), Comment. Math. Helv. 59 (1984), 651-676 (= Oeuvres, Vol. III, 675-700). 
  13. [S3] J.-P. Serre, Corps locaux, 3e éd., Hermann, Paris 1980. 
  14. [S4] J.-P. Serre, Lettre à J. Martinet du 15/11/89. 
  15. [Sp] T. A. Springer, Sur les formes quadratiques d'indice zéro, C. R. Acad. Sci. Paris 244 (1952), 1517-1519. Zbl0046.24303
  16. [W] E. Witt, Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung p f , J. Reine Angew. Math. 174 (1936), 237-245. Zbl0013.19601

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