THE DISTRIBUTION OF NUMBER FIELDS WITH WREATH PRODUCTS AS GALOIS GROUPS

Abstract

Let G be a wreath product of the form C2 ≀ H, where C2 is the cyclic group of order 2. Under mild conditions for H we determine the asymptotic behavior of the counting functions for number fields K/k with Galois group G and bounded discriminant. Those counting functions grow linearly with the norm of the discriminant and this result coincides with a conjecture of Malle. Up to a constant factor these groups have the same asymptotic behavior as the conjectured one for symmetric groups.