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Presentations of some finite simple groups

Part of: Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Dragomir Ž. Đoković
Dragomir Ž. Đoković
Affiliation:
Department of Pure Mathematics, University of WaterlooWaterloo, OntarioCanadaN2L 3G1
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Abstract

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We give new presentations of the five Mathieu groups, the simple groups J1, J2, HS, McL, Co3, and some other simple and related groups. All generators in these presentations are involutions. Our presentations are simpler than the known presentations of this type for the groups mentioned above.

MSC classification

Secondary: 20D08: Simple groups 20F05: Generators, relations, and presentations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 143 - 168
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Cannon, J. J., ‘An introduction to the group theory language Cayley’, Computational Group Theory, (Academic Press, 1984).Google Scholar
[2]Conway, J. H., ‘The miracle octad generator’, Topics in Group Theory and Computation, Proceedings of the Summer School, Galway, 1973, pp. 62–68, (Academic Press, 1977).Google Scholar
[3]Conway, J. H., ‘Hexacode and tetracode—MOG and MINIMOG’, Computational Group Theory, (Academic Press, 1984).Google Scholar
[4]Conway, J. H.. Curtis, R. T., Norton, S. P., Wilson, R. A., Atlas of Finite Groups, (Clarendon Press, Oxford, 1985).Google Scholar
[5]Curtis, R. T., ‘A new combinatorial approach to M 24’, Math. Proc. Cambridge Philos. Soc. 79 (1976), 25–42.Google Scholar
[6]Soicher, L., Presentations of some finite groups, (Ph.D. Thesis, Cambridge, 1985).Google Scholar
[7]Soicher, L., ‘Presentations for some groups related to Co 1’, preprint.Google Scholar
[8]Warboys, M. F., ‘Generators for the sporadic group Co 3 as a (2, 3, 7)-group’, Proc. Edinburgh Math. Soc. (2) 25 (1982), 65–68.Google Scholar