Abstract
Let E/ k be a Galois extension of algebraic number fields with the Galois group isomorphic to the symmetric group S n on n⩽5 letters. For any field extensions k⊆ K, L⊆ E a necessary and a sufficient condition is given for the equality N K/kK ∗=N L/kL ∗ to hold, where N K/kK ∗ is the group of norms from K to k of the elements of the multiplicative group K ∗ of K.
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