Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T07:31:13.126Z Has data issue: false hasContentIssue false
  • English
  • Français

Cross Orbits

Published online by Cambridge University Press:  01 February 2010

Peter Rowley
Peter Rowley
Affiliation:
Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, United Kingdom, [email protected]

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.

This paper contains a variety of results about the action of Con way‘s largest simple group upon the crosses in the Leech lattice. These results are tailor-made for use in ‘A Monster Graph, I'(Proc. London Math. Soc. (3) 90 (2005) 42-60), where a graph related to the Monster simple group is studied.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 219 - 265
Copyright
Copyright © London Mathematical Society 2004

References

1. Conway, J. H., ‘Three lectures on exceptional groups’, Finite simple groups (ed. Powell, M. B. and Higman, G., Academic Press, New York, 1971).Google Scholar
2. Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups (Oxford Univ. Press, London, 1985).Google Scholar
3. Curtis, R. T., ‘On the Matthieu group M24 and related topics’, Ph.D. Thesis, University of Cambridge, (1972).Google Scholar
4. Curtis, R. T., ‘A new combinatorial approach to M24, Math. Proc. Cambridge Philos. Soc. 79 (1976) 25–42.Google Scholar
5. Ivanov, A. A., Geometry of sporadic groups I, Petersen and tilde geometries, Encyclopedia Math. Appl. 76 (Cambridge Univ. Press, Cambridge, 1999).Google Scholar
6. Ronan, M. A. and SMITH, S. D., ‘2-Local geometries for some sporadic groups’, Finite groups (Santa Cruz Conf. 1979), Proc. Sympos. Pure Math. 37 (Amer. Math. Soc, Providence, RI, 1980) 283–289.Google Scholar
7. Ronan, M. A. and Stroth, G., ‘Minimal parabolic geometries for the sporadic groups’, European J. Comb. 5 (1984) 59–91.Google Scholar
8. Rowley, P., ‘A Monster Graph I’, Proc. London Math. Soc, to appear.Google Scholar
9. SEGEV, Y., ‘On the uniqueness of the Co 1 2-local geometry‘, Geom. Dedicata 25 (1988) 159–219.Google Scholar