On a question of M. Conder

M. Chiara Tamburini; Paola Zucca

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: 1, page 5-7
  • ISSN: 1120-6330

Abstract

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We show that the special linear group S L 3 , Z , over the integers, is not 2 , 3 -generated. This gives a negative answer to a question of M. Conder.

How to cite

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Tamburini, M. Chiara, and Zucca, Paola. "On a question of M. Conder." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.1 (2000): 5-7. <http://eudml.org/doc/252322>.

@article{Tamburini2000,
abstract = {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.},
author = {Tamburini, M. Chiara, Zucca, Paola},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Linear Groups; Simple groups; (2,3)-generation; linear groups over the integers; -generated groups},
language = {eng},
month = {3},
number = {1},
pages = {5-7},
publisher = {Accademia Nazionale dei Lincei},
title = {On a question of M. Conder},
url = {http://eudml.org/doc/252322},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Tamburini, M. Chiara
AU - Zucca, Paola
TI - On a question of M. Conder
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/3//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 1
SP - 5
EP - 7
AB - 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.
LA - eng
KW - Linear Groups; Simple groups; (2,3)-generation; linear groups over the integers; -generated groups
UR - http://eudml.org/doc/252322
ER -

References

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  2. Di Martino, L. - Tamburini, M. C. - Zalesskii, A., On Hurwitz groups of low rank. To appear. Zbl0989.20040MR1785508DOI10.1080/00927870008827163
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  6. Lucchini, A. - Tamburini, M. C., Classical groups of large rank as Hurwitz groups. J. Algebra, 219, 1999, 531-546. Zbl1063.20504MR1706821DOI10.1006/jabr.1999.7911
  7. Lucchini, A. - Tamburini, M. C. - Wilson, J. S., Hurwitz groups of large rank. To appear. Zbl0953.20024MR1745399DOI10.1112/S0024610799008467
  8. Mazurov, V. D. - Khukhro, E. I., Unsolved Problems in Group Theory. 14° edition, The Kourovka Notebook, Novosibirsk1999. Zbl0831.20003MR1733915
  9. Miller, G. A., On the groups generated by two operators. Bull. AMS, 7, 1901, 424-426. MR1557828JFM32.0145.03
  10. Robinson, D., The Theory of Groups. Springer-Verlag1982. MR648604
  11. Tamburini, M. C. - Wilson, J. S. - Gavioli, N., On the 2 , 3 -generation of some classical groups I. J. Algebra, 168, 1994, 353-370. Zbl0819.20053MR1289105DOI10.1006/jabr.1994.1234
  12. Wilson, J. S., Simple images of triangle groups. Quart. J. Math. Oxford, Ser. (2), 50, n. 200, 1999, 523-531. Zbl0944.20032MR1728423DOI10.1093/qjmath/50.200.523

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