Locally solvable maximal subgroups in division rings
Rings and Algebras
2024-01-02 v3 Group Theory
Abstract
Let be a division ring with center , and an almost subnormal subgroup of . In this paper, we show that if contains a non-abelian locally solvable maximal subgroup, then must be a cyclic algebra of prime degree over . Moreover, it is proved that every locally nilpotent maximal subgroup of is abelian.
Cite
@article{arxiv.1908.04925,
title = {Locally solvable maximal subgroups in division rings},
author = {Huynh Viet Khanh and Bui Xuan Hai},
journal= {arXiv preprint arXiv:1908.04925},
year = {2024}
}
Comments
This version[v3] was accepted for publication in Kyoto Journal of Mathematics in 2022. Comparing to the version v2, the title of the paper has been changed and some theorems were renumbered. The version v2 was entitled "On almost subnormal subgroups in division rings". Also, the two main results Theorems 3.10 and 3.11 in v2 were renumbered as Theorems 1.1 and 1.2 in the accepted version v3