Malle's Conjecture for $G\times A$, with $G=S_3,S_4,S_5$

Abstract

We prove Malle's conjecture for $G\times A$, with $G=S_3,S_4,S_5$ and $A$ an abelian group. This builds upon work of the fourth author, who proved this result with restrictions on the primes dividing $A$.