engleski

Determining elements of minimal index in an infinite family of totally real bicyclic biquadratic number fields

Let c ≠ 2 be a positive integer such that c and c + 4 are square-free. We consider the infinite parametric family of bicyclic biquadratic fields K = Q(sqrt {; ; ; 2c}; ; ; , sqrt {; ; ; 2(c + 4)}; ; ; ). We determine the integral basis of the field. We show that K admits no power integral basis, determine the minimal index and all elements of minimal index. We use the solutions of a parametric family of quartic Thue equations and extensive numerical calculations by Maple and Magma are also involved.

bicyclic biquadratic fields ; power integral basis ; minimal index

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