  We correct the faulty formulas given in a previous article and we compute the
defect group for the Iwasawa $\lambda$ invariants attached to the S-ramified
T-decomposed a belian pro-${\ell}$-extensions on the Z${\ell}$-cyclotomic
extensionof a number field. As a consequence, we extend the results of Itoh,
Mizusawa and Ozaki on tamely ramified Iwasawa modules for the cyclotomic
Z${\ell}$-extension of abelian fields.
