Restricting the Splitting Types of a Positive Density Set of Places in Number Field Extensions

2023/09/21 by Alberts, Brandon
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.12525

Abstract

We prove necessary and sufficient conditions for a finite group G with an ordering of G-extensions to satisfy the following property: for every positive density set of places A of a number field K and every splitting type given by a conjugacy class c in G, 0% of G-extensions avoid this splitting type for each p∈ A.

Related

• Counting G-Extensions by Discriminant
• Split extensions of group with infinite conjugacy classes
• Extensions of group schemes of μ-type by a constant group scheme
• On characterisation of a finite group by the set of conjugacy class sizes
• Unramified extensions over low degree number fields