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Every $\text{PSL}_{2}(13)$ in the Monster contains $13A$-elements

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 November 2015

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 [email protected]

Abstract

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We prove the assertion in the title by conducting an exhaustive computational search for subgroups isomorphic to $\text{PSL}_{2}(13)$ and containing elements in class $13B$.

Supplementary materials are available with this article.

MSC classification

Primary: 20D08: Simple groups
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 667 - 674
Copyright
© The Author 2015 

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, 1985).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., ‘On subgroups of the Monster containing A 5 ’s’, J. Algebra 319 (2008) 2653–2667.CrossRefGoogle Scholar
Norton, S., ‘Anatomy of the Monster: I’, Proceedings of the Atlas Ten Years on Conference, Birmingham, 1995 (Cambridge University Press, 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 L 2(41), and a new Moonshine phenomenon’, J. Lond. Math. Soc. (2) 87 (2013) 943–962.Google Scholar
Wilson, R. A., The finite simple groups , Graduate Texts in Mathematics 251 (Springer, 2009).CrossRefGoogle Scholar
Wilson, R. A., ‘Classification of subgroups isomorphic to PSL2(27) in the Monster’, LMS J. Comput. Math. 17 (2014) 33–46.Google Scholar
Wilson, R. A. et al. , ‘An atlas of group representations’, http://brauer.maths.qmul.ac.uk/Atlas/.Google Scholar
Supplementary material: File

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