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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Submitted on : Monday, March 14, 2016 - 3:34:35 PM
Last modification on : Monday, March 4, 2019 - 2:04:19 PM

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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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