Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T13:28:44.402Z Has data issue: false hasContentIssue false

The string of nets

Published online by Cambridge University Press:  05 December 2012

Simon P. Norton*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK (s.norton@dpmms.cam.ac.uk)
Rights & Permissions [Opens in a new window]

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.

After summarizing from previous papers the definitions of the concepts associated with nets, i.e. triples of 6-transpositions in the Monster up to braiding, we give some results.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2012

References

1.Conway, J. H., A simple construction for the Fischer–Griess monster group, Invent. Math. 79 (1985), 513540.CrossRefGoogle Scholar
2.Conway, J. H. and Hsu, T. M., Quilts and T-systems, J. Alg. 174 (1995), 856903.CrossRefGoogle Scholar
3.Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups: maximal subgroups and ordinary characters for simple groups (Oxford University Press, 1985).Google Scholar
4.Hsu, T. M., Quilts, T-systems and the combinatorics of Fuchsian groups, PhD Thesis, Princeton University (1994).Google Scholar
5.Hsu, T. M., Quilts, the 3-string braid group, and braid actions on finite groups: an introduction, in The Monster and Lie algebras (ed. Ferrar, J. and Harada, K.), Volume 7, pp. 8597 (Walter de Gruyter, 1998).CrossRefGoogle Scholar
6.Hsu, T. M., Quilts: central extensions, braid actions, and finite groups, Springer Lecture Notes, Volume 1731 (Springer, 2000).CrossRefGoogle Scholar
7.Norton, S., Generalized moonshine, Proceedings of Symposia in Pure Mathematics, Volume 47, pp. 208209 (American Mathematical Society, Providence, RI, 1987).Google Scholar
8.Norton, S., The Monster algebra: some new formulae, in Moonshine, the Monster and related topics (ed. Dong, C. and Mason, G.), Contemporary Mathematics, Volume 193, pp. 297306 (American Mathematical Society, Providence, RI, 1996).CrossRefGoogle Scholar
9.Norton, S., Anatomy of the Monster, I, in Proc. Conf. Atlas: Ten Years On, Birmingham, 1995, pp. 198214 (Cambridge University Press, 1998).Google Scholar
10.Norton, S., Netting the Monster, in The Monster and Lie alegbras (ed. Ferrar, J. and Harada, K.), Volume 7, pp. 111125 (Walter de Gruyter, 1998).CrossRefGoogle Scholar
11.Norton, S., Counting nets in the Monster, in Groups, combinatorics and geometry (ed. Ivanov, A. A., Liebeck, M. W. and Saxl, J.), pp. 227232 (World Scientific, 2003).CrossRefGoogle Scholar
12.Schönert, M. and the GAP Group, GAP4 Manual (groups, algorithms and programming) (Lehrstuhl D für Mathematik, RWTH Aachen, 2000).Google Scholar