On the \((2,3,7)\)-generation of some special linear groups. (English) Zbl 1092.20031
Tamburini, Wilson and the reviewer proved that for each prime power \(q\) and each integer \(n\geq 287\) (and also for 93 other integers smaller than 287), \(\text{SL}_n(q)\) and \(\text{SL}_n(\mathbb{Z})\) are \((2,3,7)\)-generated. In this paper the author extends these results to 50 other additional values of \(n\leq 287\). Results in this direction have been also obtained by M. Vsemirnov [LMS J. Comput. Math. 7, 300-336 (2004; Zbl 1080.20049)].
Reviewer: Andrea Lucchini (Brescia)
MSC:
| 20F05 | Generators, relations, and presentations of groups |
| 20G40 | Linear algebraic groups over finite fields |
| 20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |
Citations:
Zbl 1080.20049References:
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