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Generating finite completely reducible linear groups


Authors: L. G. Kovács and Geoffrey R. Robinson
Journal: Proc. Amer. Math. Soc. 112 (1991), 357-364
MSC: Primary 20H20
DOI: https://doi.org/10.1090/S0002-9939-1991-1047004-0
MathSciNet review: 1047004
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Abstract: It is proved here that each finite completely reducible linear group of dimension $ d$ (over an arbitrary field) can be generated by $ \left\lfloor {\frac{3}{2}d} \right\rfloor $ elements. If a finite linear group $ G$ of dimension $ d$ is not completely reducible, then its characteristic is a prime, $ p$ say, and the factor group of $ G$ modulo the largest normal $ p$-subgroup $ {\mathbb{O}_p}\left( G \right)$ may be viewed as a completely reducible linear group acting on the direct sum of the composition factors of the natural module for $ G$: consequently, $ G/{\mathbb{O}_p}\left( G \right)$ can still be generated by $ \left\lfloor {\frac{3}{2}d} \right\rfloor $ elements.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1047004-0
Article copyright: © Copyright 1991 American Mathematical Society

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