On the image-rank of abelian extensions with restricted ramification [Journal of Number Theory 92 (2002) 376–404]

In the original Section 3.3, the main result is Theorem 29. In the proof of this Theorem, we use the fact that the cyclotomic extension k∞ is not contained in image (except for the trivial case image). In fact, there is one other exception: the imaginary quadratic field. Moreover, there were some imprecisions in Proposition 28. In this note, we clarify all of this and we produce the complete proof of the key result.