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Let be a prime number and be a number field. Since Iwasawa’s works, the behaviour of the -part of the ideal class group in the -extensions of has been well understood. Moreover, M. Grandet and J.-F. Jaulent gave a precise result about its abelian -group structure.On the other hand, the ideal class group of a number field may be identified with the torsion part of the of its ring of integers. The even -groups of rings of integers appear as higher versions of the class group. Many authors...