Hostname: page-component-6bb9c88b65-6vlrh Total loading time: 0 Render date: 2025-07-17T14:16:52.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Classification of subgroups isomorphic to $\mathrm{PSL}_2(27)$ in the Monster

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 April 2014

Robert A. Wilson
Robert A. Wilson*
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom email R.A.Wilson@qmul.ac.uk

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.

As a contribution to an eventual solution of the problem of the determination of the maximal subgroups of the Monster we prove that the Monster does not contain any subgroup isomorphic to $\mathrm{PSL}_2(27)$.

Supplementary materials are available with this article.

MSC classification

Secondary: 20D08: Simple groups

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 33 - 46
Copyright
© The Author 2014 

References

Bray, J. N., ‘An improved method for generating the centralizer of an involution’, Arch. Math. (Basel) 74 (2000) 241–245.Google Scholar
Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., An atlas of finite groups (Oxford University Press, Oxford, 1985).Google Scholar
Holmes, P. E., ‘A classification of subgroups of the Monster isomorphic to $S_4$ and an application’, J. Algebra 319 (2008) 3089–3099.Google Scholar
Holmes, P. E., Linton, S. A., O’Brien, E. A., Ryba, A. J. E. and Wilson, R. A., ‘Constructive membership in black-box groups’, J. Group Theory 11 (2008) 747–763.Google Scholar
Holmes, P. E. and Wilson, R. A., ‘A new maximal subgroup of the Monster’, J. Algebra 251 (2002) 435–447.Google Scholar
Holmes, P. E. and Wilson, R. A., ‘A new computer construction of the Monster using 2-local subgroups’, J. Lond. Math. Soc. (2) 67 (2003) 349–364.Google Scholar
Holmes, P. E. and Wilson, R. A., ‘ $\mathrm{PSL}_2(59)$ is a subgroup of the Monster’, J. Lond. Math. Soc. (2) 69 (2004) 141–152.Google Scholar
Holmes, P. E. and Wilson, R. A., ‘On subgroups of the Monster containing $A_5$ ’s’, J. Algebra 319 (2008) 2653–2667.Google Scholar
Linton, S. A., Parker, R. A., Walsh, P. G. and Wilson, R. A., ‘Computer construction of the Monster’, J. Group Theory 1 (1998) 307–337.Google Scholar
Norton, S., ‘Anatomy of the Monster: I’, Proceedings of the Atlas Ten Years on Conference, Birmingham, 1995 (Cambridge University Press, Cambridge, 1998) 198–214.Google Scholar
Norton, S. P. and Wilson, R. A., ‘Anatomy of the Monster: II’, Proc. Lond. Math. Soc. (3) 84 (2002) 581–598.Google Scholar
Norton, S. P. and Wilson, R. A., ‘A correction to the 41-structure of the Monster, a construction of a new maximal subgroup $\mathrm{PSL}_2(41)$ , and a new Moonshine phenomenon’, J. Lond. Math. Soc. (2) 87 (2013) 943–962; doi:10.1112/jlms/jds078.CrossRefGoogle Scholar
Wilson, R. A., ‘Is $J_1$ a subgroup of the Monster?’, Bull. Lond. Math. Soc. 18 (1986) 349–350.Google Scholar
Wilson, R. A., ‘The odd-local subgroups of the Monster’, J. Aust. Math. Soc. (A) 44 (1988) 1–16.Google Scholar
Wilson, R. A., The finite simple groups , Graduate Texts in Mathematics 251 (Springer, 2009).Google Scholar
Wilson, R. A. et al. , ‘An atlas of group representations’, http://brauer.maths.qmul.ac.uk/Atlas/.Google Scholar
Supplementary material: File

Wilson Supplementary Material

Supplementary Material

Download Wilson Supplementary Material(File)
File 2.6 MB