Locally solvable maximal subgroups in division rings

Let $D$ be a division ring with center $F$, and $G$ an almost subnormal subgroup of $D^*$. In this paper, we show that if $G$ contains a non-abelian locally solvable maximal subgroup, then $D$ must be a cyclic algebra of prime degree over $F$. Moreover, it is proved that every locally nilpotent maximal subgroup of $G$ is abelian.

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