Isomorphisms of Galois groups of number fields with restricted ramification
Ryoji Shimizu · Mathematische Nachrichten · 2023
Abstract Let K be a number field and S a set of primes of K . We write for the maximal extension of K unramified outside S and for its Galois group. In this paper, we answer the following question under some assumptions: “For , let be a number field, a (sufficiently large) set of primes of and an isomorphism. Is σ induced by a unique isomorphism between and ?” Here, the main assumption is about the Dirichlet density of .