The Ramanujan Journal
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 PSL₂(7) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2³:GL₃(2) of smallest absolute discriminant.
© Springer Science+Business Media, LLC, part of Springer Nature 2018
John W. Jones and David P. Roberts. Mixed degree number field computations. The Ramanujan Journal 47 (2018), no. 1, 47-66.
This is a pre-print of an article published in The Ramanujan Journal. The final authenticated version is available online at: https://doi.org/10.1007/s11139-018-0024-9