Mixed degree number field computations

John Jones, David P. Roberts

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)47-66
Number of pages20
JournalRamanujan Journal
Volume47
Issue number1
DOIs
StatePublished - Oct 1 2018

Keywords

  • Discriminant
  • Galois group
  • Number field
  • Ramification

ASJC Scopus subject areas

  • Algebra and Number Theory

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