Let F be a number field and let p be an odd prime. Denote by S the set of p-adic and infinite places of F. We study a generalization to K-theory of the Kummer-Leopoldt constant for the S-units introduced in [7, Section 4]. We express in particular its value as the exponent of some Galois module. As an application, we give a new characterization of (p,i)-regular quadratic number fields.

We thank the referee for his/her valuable comments and suggestions which improved the quality of this work.