Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T11:49:43.304Z Has data issue: false hasContentIssue false
  • English
  • Français

Matrix generators for Fischer's group Fi24

Published online by Cambridge University Press:  24 October 2008

Robert A. Wilson
Robert A. Wilson
Affiliation:
School of Mathematics and Statistics, The University of Birmingham, Edgbaston, Birmingham B15 2TT
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we show how to construct 781 × 781 matrices over GF(3), generating the largest of the three Fischer groups. For some purposes these are more useful than the permutations on 306936 points, as they require only one-sixth of the storage space. We also construct generators for its triple cover, as 1566 × 1566 matrices over GF(2), and for the derived group thereof, as 783 × 783 matrices over GF(4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 1 , January 1993 , pp. 5 - 8
Copyright
Copyright © Cambridge Philosophical Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A.. An ATLAS of Finite Groups (Oxford University Press, 1985).Google Scholar
[2]Fischer, B.. Finite groups generated by 3-transpositions. (Preprint), Warwick University.CrossRefGoogle Scholar
[3]Linton, S. A.. The maximal subgroups of the Thompson group. J. London Math. Soc. (2) 39 (1989), 79–88.CrossRefGoogle Scholar
[4]Linton, S. A. and Wilson, R. A.. The maximal subgroups of the Fischer groups Fi24 and Fi24. Proc. London Math. Soc. (3) 63 (1991), 113–164.CrossRefGoogle Scholar
[5]Meyer, W., Neutsch, W. and Parker, R. A.. The minimal 5-representation of Lyons' sporadic simple group. Math. Ann. 272 (1985), 29–39.CrossRefGoogle Scholar
[6]Norton, S. P.. The construction of J 4. In The Santa Cruz Conference on Finite Groups (ed. Cooperstein, B. N. and Mason, G.), (American Mathematical Society, 1980). pp. 271–278.Google Scholar
[7]Norton, S. P.. F and other simple groups. Ph.D. thesis, Cambridge University (1975).Google Scholar
[8]Norton, S. P.. On the group Fi24. Geom. Dedicata 25 (1988), 483–501.CrossRefGoogle Scholar
[9]Parker, R. A.. The computer calculation of modular characters (The ‘Meat-axe’). In Computational Group Theory (ed. Atkinson, M. D.), (Academic Press. 1984), pp. 267–274.Google Scholar
[10]Parker, R. A. and Wilson, R. A.. The computer construction of matrix representations of finite groups over finite fields. J. Symb. Comp. 9 (1990), 583–590.CrossRefGoogle Scholar
[11]Ryba, A. J. E.. A new construction of the O'Nan group. J. Algebra 112 (1988). 173–197.CrossRefGoogle Scholar
[12]Ryba, A. J. E. and Wilson, R. A.. Matrix generators for the Harada-Norton group. Submitted for publication.Google Scholar
[13]Wilson, R. A.. The Brauer tree for J 3 in characteristic 17. J. Symb. Comp., to appear.Google Scholar
[14]Wilson, R. A.. Some subgroups of the Baby Monster. Invent. Math. 89 (1987), 197–218.CrossRefGoogle Scholar
[15]Wilson, R. A.. A new construction of the Baby Monster and its applications. Bull. London Math. Soc., to appear.Google Scholar