  We are interested in classical and logarithmic imaginary classes of abelian
number fields in connection with Iwasawa theory. For any given odd prime
${\ell}$ and any imaginary abelian number field K, we compute the isotypic
components of the logarithmic ${\ell}$-class group of K associated to imaginary
irreducible ${\ell}$-adic characters of its Galois group and we extend to this
situation the Gold criterium on lambda invariants. We first study the
semi-simple case, thus the non semi-simple case in connection with transition
formulas of genus for supercircular fields.
