Unramified extensions of quadratic number fields with Galois group $2.A_n$
Acta Arithmetica
MSC: Primary 12F12; Secondary 11R21, 11R29
DOI: 10.4064/aa250506-23-9
Published online: 22 December 2025
Abstract
We realize infinitely many covering groups $2.A_n$ (where $A_n$ is the alternating group) as the Galois groups of everywhere unramified Galois extensions over infinitely many quadratic number fields. After several predecessor works investigating special cases or proving conditional results in this direction, these are the first unramified realizations of infinitely many of these groups.
