Abstract
Following results by R. Schoof and by H.W. Lenstra–R. Schoof, we give a method allowing to find, for all prime p not dividing [F:ℚ], a system of generators of the relative p-class group of the imaginary abelian field F, only with the knowledge of Bernoulli numbers B 1 (ψ -1 ). Numerical examples are given for p=3 and p=5 about cyclic extensions of degrees 2 and 4. The first example of p-class group having a non cyclic χ-component (for a ℚ p -irreducible odd and not quadratic character χ) has been found by T. Berthier for p=5, and the cyclic quartic field of conductor 37×51 containing ℚ(37).
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