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.
|Number of pages||10|
|Journal||Israel Journal of Mathematics|
|State||Published - 2002|
ASJC Scopus subject areas
- Mathematics (all)