Abstract
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.
Original language | English (US) |
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Pages (from-to) | 47-66 |
Number of pages | 20 |
Journal | Ramanujan Journal |
Volume | 47 |
Issue number | 1 |
DOIs | |
State | Published - Oct 1 2018 |
Bibliographical note
Funding 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.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Discriminant
- Galois group
- Number field
- Ramification