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Hurwitz Groups of Intermediate Rank

Published online by Cambridge University Press:  01 February 2010

M. Vsemirnov
Affiliation:
Sidney Sussex College, Sidney Street, Cambridge CB2 3HU, United Kingdom, [email protected], [email protected], http://logic.pdmi.ras.ru/~vsemir

Abstract

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This paper is concerned with (2, 3, 7)-generated linear groups of ranks less than 287. In particular, sixty new values of n are found, such that the groups SLn (q) are Hurwitz for any prime power q. This result provides the next step in deciding which classical groups are Hurwitz.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2004

References

1. Conder, M. D. E., ‘Generators for alternating and symmetric groups’, J. London Math. Soc(2) 22 (1980) 7586.CrossRefGoogle Scholar
2. Di Martino, L. and Tamburini, M. C., ‘On the (2,3,7)-generation of maximal parabolic subgroups’, J. Austral. Math. Soc.71(2001) 187199.CrossRefGoogle Scholar
3. Di Martino, L. and Tamburini, M. C. and Zalesski, A. E., ‘On Hurwitz groups of low rank’, Comm. Algebra 28 (2000)53835404.CrossRefGoogle Scholar
4. Hahn, A. J. and Meara, O.T.O.', The classical groups and K-theory (Springer, 1989).Google Scholar
5. Jordan, C., ‘Sur la limite de transivité des groupes non alternés’, Bull. Soc. Math. France 1 (1873)4071.CrossRefGoogle Scholar
6. Lucchini, A. and Tamburini, M. C., ‘Classical groups of large rank as Hurwitz groups’,J. Algebra 219 (1999) 531546.CrossRefGoogle Scholar
7. Lucchini, A. and Tamburini, M. C. and Wilson, J. S., ‘Hurwitz groups of large rank’, J. London Math. Soc(2) 61 (2000) 8192.CrossRefGoogle Scholar
8. Scott, L. L., ‘Matrices and cohomology’, Ann. of Math 105 (1977) 473492.CrossRefGoogle Scholar
9. Stothers, W. W., ‘Subgroups of the (2,3,7)-triangle group’, Manuscripta Math 20 (1977) 323334.CrossRefGoogle Scholar
10. Tamburini, M. C. and Vsemirnov, M., ‘Hurwitz groups and Hurwitz generation’, Handbook of Algebra vol. 4, to appear.Google Scholar
11. Wielandt, H., Finite permutation groups (Academic Press, 1964).Google Scholar
Supplementary material: File

JCM 7 Vsemirnov Appendix C

Vsemirnov Appendix C

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