Galois Groups and the Multiplicative Structure of Field Extensions

Abstract

Let K/k be a finite Galois field extension, and assume k is not an algebraic extension of a finite field.Let K* be the multiplicative group of K , and let &{K/k) be the product of the multiplicative groups of the proper intermediate fields.The condition that the quotient group T = K*/Q(K/k) be torsion is shown to depend only on the Galois group G .For algebraic number fields and function fields, we give a complete classification of those G for which T is nontrivial.

Locations

• Transactions of the American Mathematical Society - View - PDF