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

On S-ramified T-split Iwasawa modules