Hostname: page-component-669899f699-chc8l Total loading time: 0 Render date: 2025-04-26T04:10:16.311Z Has data issue: false hasContentIssue false
  • English
  • Français

Conjugacy Class Representatives in the Monster Group

Published online by Cambridge University Press:  01 February 2010

R. W. Barraclough  and
R. A. Wilson
R. W. Barraclough
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London El 4NS, [email protected], http://www.maths.qmul.ac.uk/~raw
R. A. Wilson
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London El 4NS, [email protected], http://www.maths.qmul.ac.uk/~raw

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.

The paper describes a procedure for determining (up to algebraic conjugacy) the conjugacy class in which any element of the Monster lies, using computer constructions of representations of the Monster in characteristics 2 and 7. This procedure has been used to calculate explicit representatives for each conjugacy class.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 8 , 2005 , pp. 205 - 216
Copyright
Copyright © London Mathematical Society 2005

References

1.Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., of finite groups (Oxford University Press, 1985; reprinted with corrections, 2004).Google Scholar
2.Conway, J. H. and Norton, S. P., ‘Monstrous moonshine’, Bull. London Math. Soc. 11 (1979) 308–339.CrossRefGoogle Scholar
3.Holmes, P. E., Linton, S. A. and Murray, S. H., ‘Product replacement in the monster’, Experiment. Math. 12 (2003) 123–126.CrossRefGoogle Scholar
4.Linton, S. A., Parker, R. A., Walsh, P. and Wilson, R. A., ‘Computer construction of the monster’, J. Group Theory 1 (1998) 307–337.Google Scholar
5.Suleiman, I. A. I., Walsh, P. G. and Wilson, R. A., ‘Conjugacy classes in sporadic simple groups’, Comm Alvebra 28 (2000) 3709–3222.Google Scholar
6.Wilson, R. A., ‘Standard generators for sporadic simple groups’, J. Algebra 184 (1996) 505–515.CrossRefGoogle Scholar
7.Wilson, R. A., ‘A construction of the monster group over GF(7) and an application’, preprint, University of Birmingham, 2000; http://web.mat.bham.ac.uk/R.A.Wilson/pubs/Mcon7.html.Google Scholar
8.Wilson, R. A., ‘Conjugacy class representatives in Fischer's baby monster’, LMSJ. Comput. Math. 5 (2002) 175–180.CrossRefGoogle Scholar
9.Wilson, R. A. et al. , ‘A world wide web atlas of group representations’ (1995–2005), http://brauer.maths.qmul.ac.uk/Atlas/.Google Scholar
Supplementary material: File

JCM 8 Barraclough and Wilson Appendix A

Barraclough and Wilson Appendix A

Download JCM 8 Barraclough and Wilson Appendix A(File)
File 2.2 MB
Supplementary material: File

JCM 8 Barraclough and Wilson Appendix A readme

Barraclough and Wilson Appendix A readme.txt

Download JCM 8 Barraclough and Wilson Appendix A readme(File)
File 1.3 KB