The Ramanujan Journal

, Volume 47, Issue 1, pp 47–66 | Cite as

Mixed degree number field computations

  • John W. JonesEmail author
  • David P. Roberts


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 \({{\mathrm{PSL}}}_2(7)\) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group \(2^3{:}{{\mathrm{GL}}}_3(2)\) of smallest absolute discriminant.


Number field Galois group Discriminant Ramification 

Mathematics Subject Classification

Primary: 11R21 Secondary: 11Y40 11R32 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA
  2. 2.Division of Science and MathematicsUniversity of Minnesota-MorrisMorrisUSA

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