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I know that for $n>2$, $n-2$ transposition cannot generate $S_n$,but I want to know for $SL(n,q)$ is true or not? Why?

For $n>2$ ,$n-2$ transvections cannot generate $SL(n,q)$.

Any idea?

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Fill in the blanks: Each transvection fixes a [...]. The intersection of $n-2$ [...] is nonzero. For every nonzero vector, there exists an element of $\mathrm{SL}\left(n,q\right)$ which does not [...] it. Contradiction. – darij grinberg Mar 27 '12 at 21:27
great thanks [hyperplane] – Babgen Mar 28 '12 at 5:07

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