Restricting the splitting types of a positive density set of places in number field extensions

Abstract

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