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.
Categories: math.NT