Frattini closed groups and adequate extensions of global fields

David B. Leep, Tara L. Smith, Ronald Solomon

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let L be a finite Galois extension of a global field F. It is shown that if the Galois group G = Gal(L/F) satisfies a certain condition, then L is a maximal commutative subfield of some F-division algebra if and only if the intermediate field corresponding to the Frattini subgroup of G is also a maximal commutative subfield of some F-division algebra. In particular this condition holds if G is a supersolvable group.

Original languageEnglish
Article numberBF02764067
Pages (from-to)1-10
Number of pages10
JournalIsrael Journal of Mathematics
Volume130
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics (all)

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