Geodesic
On a question of M. Conder
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 1, pp. 5-7.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We show that the special linear group \( SL(3, \mathbb{Z}) \), over the integers, is not \( (2,3) \)-generated. This gives a negative answer to a question of M. Conder.
Dimostriamo che il gruppo speciale lineare \( SL(3, \mathbb{Z}) \), sugli interi, non è \( (2,3) \)-generato. 
@article{RLIN_2000_9_11_1_a0,
     author = {Tamburini, M. Chiara and Zucca, Paola},
     title = {On a question of {M.} {Conder}},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {5--7},
     publisher = {mathdoc},
     volume = {Ser. 9, 11},
     number = {1},
     year = {2000},
     zbl = {0983.20045},
     mrnumber = {604811},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_1_a0/}
}
TY  - JOUR
AU  - Tamburini, M. Chiara
AU  - Zucca, Paola
TI  - On a question of M. Conder
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 2000
SP  - 5
EP  - 7
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_1_a0/
LA  - en
ID  - RLIN_2000_9_11_1_a0
ER  - 
%0 Journal Article
%A Tamburini, M. Chiara
%A Zucca, Paola
%T On a question of M. Conder
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 2000
%P 5-7
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_1_a0/
%G en
%F RLIN_2000_9_11_1_a0
Tamburini, M. Chiara; Zucca, Paola. On a question of M. Conder. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 1, pp. 5-7. http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_1_a0/

[1] J. Cohen, On non-Hurwitz groups. Glasgow Math. J., 22, 1981, 1-7. | DOI | MR | Zbl

[2] L. Di Martino - M. C. Tamburini - A. Zalesskii, On Hurwitz groups of low rank. To appear. | DOI | MR | Zbl

[3] D. Garbe, Uber eine Classe von arithmetisch definierbaren Normalteilern der Modulgruppe. Math. Ann., 235, 1978, 195-215. | fulltext EuDML | MR | Zbl

[4] M. W. Liebeck - A. Shalev, Classical groups, probabilistic methods and the \( (2,3) \)-generation problem. Ann. Math., 144, 1996, 77-125. | DOI | MR | Zbl

[5] A. Lucchini, \( (2,3,k) \)-generated groups of large rank. Arch. Math. (Basel), 73, n. 4, 1999, 241-248. | DOI | MR | Zbl

[6] A. Lucchini - M. C. Tamburini, Classical groups of large rank as Hurwitz groups. J. Algebra, 219, 1999, 531-546. | DOI | MR | Zbl

[7] A. Lucchini - M. C. Tamburini - J. S. Wilson, Hurwitz groups of large rank. To appear. | DOI | MR | Zbl

[8] V. D. Mazurov - E. I. Khukhro, Unsolved Problems in Group Theory. 14° edition, The Kourovka Notebook, Novosibirsk 1999. | MR | Zbl

[9] G. A. Miller, On the groups generated by two operators. Bull. AMS, 7, 1901, 424-426. | fulltext mini-dml | Jbk 32.0145.03 | DOI | MR

[10] D. Robinson, The Theory of Groups. Springer-Verlag 1982. | MR

[11] M. C. Tamburini - J. S. Wilson - N. Gavioli, On the \( (2,3) \)-generation of some classical groups I. J. Algebra, 168, 1994, 353-370. | DOI | MR | Zbl

[12] J. S. Wilson, Simple images of triangle groups. Quart. J. Math. Oxford, Ser. (2), 50, n. 200, 1999, 523-531. | DOI | MR | Zbl