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

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arxiv 1809.00356 v2 pith:R3256LI3 submitted 2018-09-02 math.RA

Huynh Viet Khanh , Bui Xuan Hai This is my paper · ORCID
classification math.RA
keywords mathrmmaximalnotesolvablesubgroupsubgroupssubnormalalgebra
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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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  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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