Units of some abelian imaginary number fields of type (2, 4)

Abstract

Let K be an abelian imaginary number field of type (2,4), i.e. the Galois goup Gal(K ∕ ℚ) ≅ (ℤ ∕ 2 ℤ) × (ℤ ∕ 4ℤ). In this paper, we determine the fundamental system of units of some field K.