Title: Abundant central extensions of non-trivial genera
Abstract: Let k be either a local or a global field, and K be a finite Galois extension of k with g = Gal ( K/k ). Let L be a Galois extension of K which is also Galois over k . Such an extension is called central if Gal(L/iT) lies inside the centre of Gal(L/K). Clearly L is abelian over K . Next set L* = L∩K · k ab where k ab is the maximal abelian extension of k in its algebraic closure. This is the genus field of L over K/k .