Discriminants of $\mathop{\mathfrak{S}}\nolimits_n$-orders

Abstract : Let alpha be an algebraic integer of degree n >= 2. Let alpha(1),..., alpha(n) be the n complex conjugate of alpha. Assume that the Galois group Gal(Q(alpha(1),..., alpha(n))/Q) is isomorphic to the symmetric group S-n. We give a Z-basis and the discriminant of the order Z[alpha(1),..., alpha(n)]. We end up with an open question showing that this problem seems much harder when we assume that Q(alpha)/Q is already Galois or even cyclic.
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International Journal of Number Theory, World Scientific Publishing, 2016, 12 (07), pp.1899 - 1905. 〈10.1142/S1793042116501177〉
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Contributeur : Aigle I2m <>
Soumis le : lundi 14 mars 2016 - 15:34:35
Dernière modification le : mercredi 8 mars 2017 - 11:28:04

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Stéphane R. Louboutin. Discriminants of $\mathop{\mathfrak{S}}\nolimits_n$-orders. International Journal of Number Theory, World Scientific Publishing, 2016, 12 (07), pp.1899 - 1905. 〈10.1142/S1793042116501177〉. 〈hal-01288069〉

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