Non-existence of abelian maximal subgroups in cyclic division algebras
Group Theory
2026-05-11 v2
Abstract
We prove that no cyclic division algebra (in the sense of Dickson) admits an abelian maximal subgroup in its multiplicative group. This settles a special case of a long-standing conjecture of Akbari--Mahdavi-Hezavehi--Mahmudi and complements earlier results on locally nilpotent maximal subgroups and provides a new malnormality criterion for maximal subgroups.
Keywords
Cite
@article{arxiv.2603.28341,
title = {Non-existence of abelian maximal subgroups in cyclic division algebras},
author = {Huynh Viet Khanh},
journal= {arXiv preprint arXiv:2603.28341},
year = {2026}
}
Comments
I would like to withdraw the paper due to some inaccuracies