number theory

Malle's Conjecture for , with

arXiv:2004.04651

summary

The authors prove Malle’s conjecture for number fields whose Galois group is a direct product of S3, S4, or S5 with any abelian group, extending earlier results that required restrictions on the primes dividing the abelian factor.

Abstract

We prove Malle's conjecture for , with and an abelian group. This builds upon work of the fourth author, who proved this result with restrictions on the primes dividing .

Topics & keywords

#malle's conjecture#galois groups#abelian extensions#symmetric groups#asymptotic countingMalle's conjectureS3S4S5abelian groupGalois extensions
Malle's Conjecture for $G \times A$, with $G = S_3, S_4, S_5$ · wovepaper