Let K/k be a finite Galois extension of number fields with Galois group G and S a finite G-stable set of primes of K containing all archimedean primes, all primes which ramify over k and enough primes to generate the ideal class group of K. Let E denote the group of S-units of K and ΔS the kernel of the augmentation map ZS → Z sending each Z-free generator p ∈ S of the G-permutation module ZS to 1.
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