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Published online by Cambridge University Press: 05 August 2015
In this paper, we prove that the finite simple groups $\text{PSp}_{6}(q)$,
${\rm\Omega}_{7}(q)$ and
$\text{PSU}_{7}(q^{2})$ are
$(2,3)$-generated for all
$q$. In particular, this result completes the classification of the
$(2,3)$-generated finite classical simple groups up to dimension 7.