In a division ring, every locally solvable almost subnormal subgroup is central, and every non-abelian locally solvable maximal subgroup forces the ring to have dimension p^2 over its center with cyclic prime-degree structure.
A note on solvable maximal subgroups in subnormal subgroups of ${\mathrm GL}_n(D)$
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abstract
Let $D$ be a non-commutative division ring, $G$ a subnormal subgroup of ${\mathrm GL}_n(D)$. 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 $F$.
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Locally solvable maximal subgroups in division rings
In a division ring, every locally solvable almost subnormal subgroup is central, and every non-abelian locally solvable maximal subgroup forces the ring to have dimension p^2 over its center with cyclic prime-degree structure.