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

Abstract

This paper aims at studying solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup of the general skew linear group $\GL_n(D)$ 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 $[D:F]<\infty$. Also, if $F$ is an infinite field and $n\ge 5$, then every locally solvable maximal subgroup of a normal subgroup of $\GL_n(F)$ is abelian.

Accepted for publication in Publicacions Matemàtiques (UAB)

References in corpus (3)

• A note on solvable maximal subgroups in subnormal subgroups of ${\mathrm{G}L}_n(D)$
• Intersection graphs of almost subnormal subgroups in general skew linear groups
• Locally solvable maximal subgroups in division rings

Cited by in corpus (1)

• Locally solvable maximal subgroups in division rings