We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL 2(7 ) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2 3: GL 3(2 ) of smallest absolute discriminant.
Bibliographical noteFunding Information:
Roberts’ contribution was partially supported by the Simons Foundation through grant #209472 and, in its final stages, by the National Science Foundation, through grant DMS-1601350.
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
- Galois group
- Number field