Iranian Mathematical Society Title:. On normalizers of maximal subfields of division algebras Published by the Iranian Mathematical Society ON NORMALIZERS OF MAXIMAL SUBFIELDS OF DIVISION ALGEBRAS

Author, Motiee, M Motiee
2017 Bull. Iranian Math. Soc   unpublished
Here, we investigate a conjecture posed by Amiri and Ari-annejad claiming that if every maximal subfield of a division ring D has trivial normalizer, then D is commutative. Using Amitsur classification of finite subgroups of division rings, it is essentially shown that if D is finite dimensional over its center then it contains a maximal subfield with non-trivial normalizer if and only if D * contains a non-abelian soluble subgroup. This result generalizes a theorem of Mahdavi-Hezavehi and
more » ... i-Hezavehi and Tignol about cyclicity of division algebras of prime index.