Article contents
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
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.
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
$13B$.
MSC classification
Primary:
20D08: Simple groups
- Type
- Research Article
- Information
- 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
- 3
- Cited by