Locally solvable and solvable-by-finite maximal subgroups of GLn(D)

This paper aims to study solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup of the general skew linear group GLn(D) over a division ring D. It turns out that in the case where D is non-commutative, if such maximal subgroups exist, then either it is abelian or [D : F] < ∞. Also, if F is an infinite field and n ≥ 5, then every locally solvable maximal subgroup of a normal subgroup of GLn(F) is abelian

On almost subnormal subgroups in division rings

Let $D$ be a division ring with infinite center $F$, and $G$ an almost subnormal subgroup of $D^*$. In this paper, we show that if $G$ is locally solvable, then $G\subseteq F$. Also, assume that $M$ is a maximal subgroup of $G$. It is shown that if $M$ is non-abelian locally solvable, then $[D:F]=p^2$ for some prime number $p$. Moreover, if $M$ is locally nilpotent then $M$ is abelian.Comment: arXiv admin note: text overlap with arXiv:1809.0035