Locally solvable maximal subgroups in division rings

Abstract

Let $D$ be a division ring with center $F$, and $G$ an almost subnormal subgroup of $D^{\ast }$. In this paper, we show that if $G$ contains a non-abelian locally solvable maximal subgroup, then $D$ must be a cyclic algebra of prime degree over $F$. Moreover, it is proved that every locally nilpotent maximal subgroup of $G$ is abelian.

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

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• Locally solvable subnormal and quasinormal subgroups of division rings
• On multiplicative subgroups in division rings
• On free subgroups in maximal subgroups of skew linear groups
• On locally solvable subgroups in division rings
• Locally solvable and solvable-by-finite maximal subgroups of $G{L}_n(D)$

Cited by in corpus (1)

• Locally solvable and solvable-by-finite maximal subgroups of $G{L}_n(D)$