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.
Locally solvable subnormal and quasinormal subgroups of division rings
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abstract
Let $D$ be a division ring with center $F$, and $G$ a subnormal or quasinormal subgroup of $D^*$. We show that if $G$ is locally solvable, then $G$ is contained in $F$.
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2019 1verdicts
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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.