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EnglishIn this paper, we determine the finite classical simple groups of dimension n = 3, 5 which are (2,3)-generated (the cases n = 2, 4 are known). If n = 3, they are PSL_3(q), q ≠ 4, and PSU_3(q^2), q^2 ≠ 9, 25. If n = 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.
Pellegrini, M. A., Tamburini Bellani, M. C., The simple classical groups of dimension less than 6 which are (2,3)-generated, <<JOURNAL OF ALGEBRA AND ITS APPLICATIONS>>, 2015; 14 (10): N/A-N/A. [doi:10.1142/S0219498815501480] [http://hdl.handle.net/10807/67761]
| Autori: | |
| Titolo: | The simple classical groups of dimension less than 6 which are (2,3)-generated |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1142/S0219498815501480 |
| Data di pubblicazione: | 2015 |
| Abstract: | In this paper, we determine the finite classical simple groups of dimension n = 3, 5 which are (2,3)-generated (the cases n = 2, 4 are known). If n = 3, they are PSL_3(q), q ≠ 4, and PSU_3(q^2), q^2 ≠ 9, 25. If n = 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. |
| Lingua: | Inglese |
| Rivista: | |
| Citazione: | Pellegrini, M. A., Tamburini Bellani, M. C., The simple classical groups of dimension less than 6 which are (2,3)-generated, <<JOURNAL OF ALGEBRA AND ITS APPLICATIONS>>, 2015; 14 (10): N/A-N/A. [doi:10.1142/S0219498815501480] [http://hdl.handle.net/10807/67761] |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
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