On Double Covers of the Generalized Symmetrical Group imaged wreath product imagem as Galois Groups over Algebraic Number Fields K with μd subset of K Original Research Article

Let K be an algebraic number field which contains the dth roots of unity. We will prove that all double covers of the generalized symmetric group imaged wreath product imagem are realizable as a Galois group over K and over K(T), if d is odd. If d is even, we will determine all double covers of imaged wreath product imagem which can be shown to be Galois groups over K and over K(T) using Serre′s formula on trace forms. If d ≠ 1 we will use trinomials ƒ(Xd) such that the Galois group of ƒ(X) = Xm + aXl + b set membership, variant K[X] is imagem.