The simple classical groups of dimension less than 6 which are (2,3)-generated
Abstract
In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL3(q), q <> 4, and PSU3(q2), q2 <> 9, 25. If r = 5 they are PSL5(q), for all q, and PSU5(q2), q2 >= 9. Also, the soluble group PSU3(4) is not (2,3)-generated. We give explicit (2,3)-generators of the linear preimages, in the special linear groups, of the (2,3)-generated simple groups.
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