Generating finite completely reducible linear groups

Kovács, L. G.; Robinson, Geoffrey R.

doi:10.1090/S0002-9939-1991-1047004-0

Generating finite completely reducible linear groups
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by L. G. Kovács and Geoffrey R. Robinson PDF

Proc. Amer. Math. Soc. 112 (1991), 357-364 Request permission

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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