Hostname: page-component-6bb9c88b65-t28k2 Total loading time: 0 Render date: 2025-07-26T16:07:22.514Z Has data issue: false hasContentIssue false
  • English
  • Français

A 7-Local Identification of the Monster

Published online by Cambridge University Press:  11 January 2016

C. W. Parker  and
C. B. Wiedorn
C. W. Parker
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK, C.W.Parker@bham.ac.uk
C. B. Wiedorn
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK, wiedornc@for.mat.bham.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.

We identify the monster from two of its 7-constrained maximal 7-local subgroups.

Keywords

20D05

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 178 , 2005 , pp. 129 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[1] Alperin, J. L., Local representation theory, volume 11 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1986. Modular representations as an introduction to the local representation theory of finite groups.Google Scholar
[2] Bender, H., Finite groups with dihedral Sylow 2-subgroups, J. Alg., 70 (1981), no. 1, 216–228.CrossRefGoogle Scholar
[3] Bender, H. and Glauberman, G., Characters of finite groups with dihedral Sylow 2-subgroups, J. Alg., 70 (1981), no. 1, 200–215.CrossRefGoogle Scholar
[4] Brauer, R. and Suzuki, M., On finite groups of even order whose 2-Sylow group is a quaternion group, Proc. Nat. Acad. Sci. U.S.A., 45 (1959), 1757–1759.CrossRefGoogle Scholar
[5] Conway, J. H. Curtis, R. T. Norton, S. P., Parker, R. A., and Wilson, R. A., Atlas of finite groups, Clarendon Press, Oxford, 1985.Google Scholar
[6] Gorenstein, D., Finite Groups, Harper and Row, New York, 1968.Google Scholar
[7] Gorenstein, D. and Lyons, R., The local structure of finite groups of characteristic 2 type, Mem. Am. Math. Soc. 42(276), 1983, vii+731.Google Scholar
[8] Gorenstein, D., Lyons, R., and Solomon, R., The Classification of the Finite Simple Groups, Number 2, volume 40 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 1996.Google Scholar
[9] Gorenstein, R., Lyons, D., and Solomon, R., The Classification of the Finite Simple Groups, Number 3, volume 40 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 1998.Google Scholar
[10] Gorenstein, D. and Walter, J. H., The characterization of finite groups with dihedral Sylow 2-subgroups. I, J. Alg., 2 (1965), 85–151.CrossRefGoogle Scholar
[11] Gorenstein, D. and Walter, J. H., The characterization of finite groups with dihedral Sylow 2-subgroups. II, J. Alg., 2 (1965), 218–270.Google Scholar
[12] Griess, R., Meierfrankenfeld, U., and Segev, Y., A uniqueness proof for the Monster, Ann. Math., 130 (1989), 567–602.CrossRefGoogle Scholar
[13] Griess, R. L., A remark about representations of .1, Comm. Algebra, 13 (1985), 835–844.CrossRefGoogle Scholar
[14] Ho, C. Y., A new 7-local subgroup of the Monster, J. Algebra, 115 (1988), no. 2, 513–520.CrossRefGoogle Scholar
[15] Ivanov, A. A., A geometric characterization of the Monster, Groups, combinatorics & geometry (Durham, 1990), volume 165 of London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge (1992), pp. 46–62.Google Scholar
[16] Ivanov, A. A. and Meierfrankenfeld, U., Simple connectedness of the 3-local geometry of the Monster, J. Algebra, 194 (1997), no. 2, 383–407.CrossRefGoogle Scholar
[17] Jansen, C. Lux, K., Parker, R., and Wilson, R., An atlas of Brauer characters, volume 11 of London Mathematical Society Monographs, New Series, The Clarendon Press Oxford University Press, New York, 1995. Appendix 2 by Breuer, T. and Norton, S., Oxford Science Publications.Google Scholar
[18] Kleidman, P. B., The maximal subgroups of the Chevalley groups G2(q) with q odd, the Ree groups 2G2(q), and their automorphism groups, J. Algebra, 117 (1988), no. 1, 30–71.CrossRefGoogle Scholar
[19] Kurzweil, H. and Stellmacher, B., Theorie der endlichen Gruppen, Springer-Verlag, Berlin, 1998. Eine Einführung. [An introduction].CrossRefGoogle Scholar
[20] Meierfrankenfeld, U., Stellmacher, B., and Stroth, G., Finite groups of local characteristic p: An overview, Groups, combinatorics & geometry (Durham, 2001), World Sci. Publishing, River Edge, NJ (2003), pp. 155–192.Google Scholar
[21] Parker, C. W. and Rowley, P. J., A characteristic 5 identification of the Lyons group, J. London Math. Soc. (2), 69 (2004), no. 1, 128–140.CrossRefGoogle Scholar
[22] Parker, C. W. and Rowley, P. J., Symplectic Amalgams, Springer, London, 2002.CrossRefGoogle Scholar
[23] Parker, C. W. and Wiedorn, C. B., A 5-local identification of the Monster, Arch. Math., 83 (2004), 404–415.CrossRefGoogle Scholar
[24] Parker, C. W. and Wiedorn, C. B., 5-local identifications of the Harada Norton group and of the Baby Monster, in preparation (2003).Google Scholar
[25] Wilson, R. A., The odd local subgroups of the Monster, J. Austral. Math. Soc. Ser. A, 44 (1988), no. 1, 1–16.Google Scholar