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Locally solvable subnormal and quasinormal subgroups of division rings

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arxiv 1903.11216 v6 pith:27WPF5AF submitted 2019-03-27 math.RA

Le Qui Danh , Huynh Viet Khanh This is my paper · ORCID
classification math.RA
keywords divisionlocallyquasinormalsolvablesubnormalcentercontainedring
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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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  1. Locally solvable maximal subgroups in division rings

    math.RA 2019-08 conditional novelty 6.0 of 10

    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 s...

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