The simple classical groups of dimension less than 6 which are (2,3)-generated

M. A. Pellegrini; M. C. Tamburini Bellani

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arXiv · 1405.3149

The simple classical groups of dimension less than 6 which are (2,3)-generated

M. A. Pellegrini·M. C. Tamburini Bellani

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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 PSL_3(q), q <> 4, and PSU_3(q^2), q^2 <> 9, 25. If r = 5 they are PSL_5(q), for all q, and PSU_5(q^2), q^2 >= 9. Also, the soluble group PSU_3(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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BibTeX RIS

M. A. Pellegrini, M. C. Tamburini Bellani. 2014-05-13. The simple classical groups of dimension less than 6 which are (2,3)-generated. https://arxiv.org/abs/1405.3149

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