Twisted Malle's Conjecture

2025/09/20 by Choudhary, Tanav
#FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.16770

Abstract

In this paper, we use inductive methods similar to those employed in a 2025 paper by Alberts, Lemke Oliver, Wang and Wood in order to prove many new cases of the Twisted Malle's Conjecture. Previously, this conjecture had only been proven for T \trianglelefteq G where T is abelian, and for S₃^m \trianglelefteq S₃ \wr B. We prove many new examples of this conjecture, such as for A \wr M \trianglelefteq A \wr B where A is a finite abelian p-group, B is a p-group, and M is a proper abelian normal subgroup of B, and for C_p \wr M \trianglelefteq C_p \wr B, where |B| is odd and M is a proper abelian normal subgroup of B.

Citations

• Inductive methods for counting number fields
• Counting quintic fields with genus number one
• The density of discriminants of quintic rings and fields
• Safarevic's theorem on solvable groups as Galois groups

Related

• Malle's Conjecture for G × A, with G = S₃, S₄, S₅
• On Malle's conjecture for nilpotent groups, I
• On Malle's conjecture for the product of symmetric and nilpotent groups
• On the Malle conjecture and the self-twisted cover
• A refined Malle conjecture for Heisenberg groups