Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T21:52:21.029Z Has data issue: false hasContentIssue false
  • English
  • Français

Involutions in Conway's Largest Simple Group

Published online by Cambridge University Press:  01 February 2010

Chris Bates  and
Peter Rowley
Chris Bates
Affiliation:
School of Mathematics, The University of Manchester, PO Box 88, Sackville Street, Manchester M60 1QD, United Kingdom, c.bates@postgrad.manchester.ac.uk, http://personalpages.umist.ac.uk/postgrad/c.bates
Peter Rowley
Affiliation:
School of Mathematics, The University of Manchester, PO Box 88, Sackville Street, Manchester M60 1QD, United Kingdom, peter, j.rowley@manchester.ac.uk, http://www.ma.umist.ac.uk/pjr

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, the authors determine the suborbits of Conways largest simple group in its conjugation action on each of its three conjugacy classes of involutions. Matrix representatives of these suborbits are also provided in an accompanying computer file.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 337 - 351
Copyright
Copyright © London Mathematical Society 2004

References

1. Bates, C. and Rowley, P., ‘Centralizers of real elements in finite groups, Arch. Math., to appear.Google Scholar
2. Bosma, W., Cannon, J. and Playoust, C., ‘The MAGMA algebra system I: The user language’, J. Symbolic Comput. 24 (1997) 235–265.Google Scholar
3. Bray, J., ‘An improved method for generating the centralizer of an involution’, Arch. Math. 74 (2000)241–245.Google Scholar
4. Breuer, T. and Pfeiffer, G., ‘Finding possible permutation characters’, J. Symbolic Comput. 26 (1998)343–354.Google Scholar
5. Conway, J. H., ‘A simple construction for the Fischer-Griess Monster group’, Invent. Math. 79 (1985)513–540.Google Scholar
6. Conway, J. H., ‘Three lectures on exceptional groups’, Finite simple groups(Proc.Instructional Conf., Oxford, 1969)(Academic Press, London, 1971)215–247.Google Scholar
7. Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., ATLAS of finite groups(Clarendon Press, Oxford, 1985).Google Scholar
8. Conway, J. H. and Sloane, N.J.A., Sphere packings, lattices and groups, 3rd edn.,with additional contributions by Bannai, E., Borcherds, R. E., Leech, J., Norton, S. P., Odlyzko, A. M., Parker, R. A., Queen, L. and Venkov, B. B., Grund.Math.Wiss.[Fundamental Principles of Mathematical Sciences]290(Springer, New York, 1999).Google Scholar
9. Curtis, R. T., On subgroups of.0.1.Lattice stabilizers.J.Algebra 27(1973)549–573.CrossRefGoogle Scholar
10. Curtis, R. T., On subgroups of.0.II.Local structure.J.Algebra 63(1980)413–434.Google Scholar
11. Gorenstein, D., Finite groups 2nd edn(Chelsea Publishing Co., New York, 1980).Google Scholar
12. Griess, R. L., JR., ‘The friendly giant’, Invent. Math. 69 (1982)1–102.Google Scholar
13. Harada, K. and Lang, M.-L., ‘Some elliptic curves arising from the Leech lattice’, J. Algebra 125 (1989)298–310.Google Scholar
14. The Gap Group, GAP - groups, algorithms, and programming, Version 4.3, 2002, http://www.gap-system.org.Google Scholar
15. Wilson, R. A., ‘The maximal subgroups of Conway's group Co1’, J. Algebra 85 (1983)144–165.Google Scholar
16. Wilson, R., Walsh, P., Tripp, J., Suleiman, I., Rogers, S., Parker, R., Norton, S., Linton, S. and Bray, J.,‘ATLAS of finite group representations’, http://web.mat.bham.ac.Uk/atlas/v2.0/.Google Scholar