Locally solvable and solvable-by-finite maximal subgroups of $\mathrm{GL}_n(D)$

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چکیده

This paper aims at studying solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup the general skew linear group $\GL_n(D)$ over a division ring $D$. It turns out that in case where $D$ is non-commutative, if such exist, then either it abelian or $[D:F]<\infty$. Also, $F$ infinite field $n\geq 5$, every normal $\GL_n(F)$ abelian.

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ژورنال

عنوان ژورنال: Publicacions Matematiques

سال: 2022

ISSN: ['2014-4350', '0214-1493']

DOI: https://doi.org/10.5565/publmat6612203