The arithmetic lifting property for nilpotent groups

Abstract

In this thesis it is shown that every finite nilpotent group has the arithmetic lifting property over Q^ab , the maximal abelian extension of the field of rational numbers. For a group G to have the arithmetic lifting property over a field K means that every Galois extension M/K with Galois group G can be obtained from a Galois extension M'/K(t), regular over K, with Galois group G by replacing the variable t with an element of K. In particular it is shown that every finite nilpotent group can be realized regularly as Galois group over Q^ab(t).