@article {
author = {Motiee, M.},
title = {On normalizers of maximal subfields of division algebras},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {6},
pages = {2051-2056},
year = {2017},
publisher = {Springer and the Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {Here, we investigate a conjecture posed by Amiri and Ariannejad 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 Tignol about cyclicity of division algebras of prime index.},
keywords = {Division algebras,cyclic algebras,soluble groups},
url = {http://bims.iranjournals.ir/article_1082.html},
eprint = {http://bims.iranjournals.ir/article_1082_46171c8ef1baa76a91c6ee91c20ac491.pdf}
}