A note on solvable maximal subgroups in subnormal subgroups of ${\mathrm{G}L}_n(D)$

Abstract

Let $D$ be a non-commutative division ring, $G$ a subnormal subgroup of ${\mathrm{G}L}_n(D)$. In this note we show that if $G$ contains a non-abelian solvable maximal subgroup, then $n=1$ and $D$ is a cyclic algebra of prime degree over $F$.

arXiv comment9 pages

Cited by in corpus (2)

• Locally solvable and solvable-by-finite maximal subgroups of $G{L}_n(D)$
• On locally solvable subgroups in division rings