Réalisations galoisiennes explicites de certaines familles de 2-groupes
Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 2, pp. 605-630.

Dans cet article, nous construisons, pour certains 2-groupes G, des extensions galoisiennes explicites E/(T) de groupe G vérifiant E ¯=. Nous fournissons aussi des progressions arithmétiques explicites d’entiers t 0 telles que la spécialisation E t 0 / de E/(T) en t 0 soit de groupe G.

In this paper, we construct, for some 2-groups G, explicit Galois extensions E/(T) of group G with E ¯=. We also provide explicit arithmetic progressions of integers t 0 such that the specialization E t 0 / of E/(T) at t 0 has Galois group G.

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DOI : https://doi.org/10.5802/jtnb.1136
Classification : 12E30,  12F12
Mots clés : Théorie inverse de Galois, spécialisation, réalisations explicites, quaternions généralisés
@article{JTNB_2020__32_2_605_0,
     author = {Angelot Behajaina},
     title = {R\'ealisations galoisiennes explicites de certaines familles de $2$-groupes},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {605--630},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {32},
     number = {2},
     year = {2020},
     doi = {10.5802/jtnb.1136},
     language = {fr},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1136/}
}
Angelot Behajaina. Réalisations galoisiennes explicites de certaines familles de $2$-groupes. Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 2, pp. 605-630. doi : 10.5802/jtnb.1136. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1136/

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