Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T05:45:48.786Z Has data issue: false hasContentIssue false

The Minimal Degrees of Faithful Representations of the Sporadic Simple Groups and their Covering Groups

Published online by Cambridge University Press:  01 February 2010

Christoph Jansen
Affiliation:
Itergo, Informationstechnologic GmbH, Victoriaplatz 1, 40477 Düsseldorf, Germany, christoph.jansen@itergo.com

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.

The minimal degrees of faithful representations of all sporadic simple groups and their covering groups are determined in this paper.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2005

References

1.Benson, D. J., ‘The simple group J4’, PhD thesis, University of Cambridge, 1981.Google Scholar
2.Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., ATLAS of finite groups (Clarendon Press, 1985).Google Scholar
3. THE GAP GROUP, ‘GAP – groups, algorithms, and programming’, Version 4.4, 2004, http:www.gap-system.org.Google Scholar
4.Griess JR, R. L., and Smith, S. D., ‘Minimal dimensions for modular representations of the Monster’, Comm. Algebra 22 (1994) 62796294.CrossRefGoogle Scholar
5.Henke, A., Hiss, G. and Müller, J., ‘The 7-modular decomposition matrices of the sporadic O'Nan group’, J. London Math. Soc. (2) 60 (1999) 5870.CrossRefGoogle Scholar
6.Hensing, S., ‘5-modulare Zerlegungszahlen der sporadischen einfachen Gruppe C01 und ihrer Überlagerungsgruppe 2.C01’, Diplomarbeit, Universität Heidelberg, 1993.Google Scholar
7.Hiss, G., ‘The 3-modular characters of the Rudvalis group and its covering group’, Math. Comput. 62 (1994) 851863.CrossRefGoogle Scholar
8.Hiss, G., ‘Decomposition matrices of the Chevalley group F4(2) and its covering group’, Comm. Algebra 25 (1997) 25392555.CrossRefGoogle Scholar
9.Hiss, G. and Lux, K., Brauer trees of sporadic groups (Clarendon Press, Oxford, 1989).Google Scholar
10.Hiss, G. and Lux, K., with an appendix by Breuer, T., ‘The 5-modular characters of the sporadic simple Fischer groups Fi22 and Fi23, Comm. Algebra 22 (1994) 3563–3590.Google Scholar
11.Hiss, G. and Müller, J., ‘The 5-modular characters of the sporadic simple Rudvalis group and its covering group’, Comm. Algebra 23 (1995) 4633–667.CrossRefGoogle Scholar
12.Hiss, G. and White, D. L., ‘The 5-modular characters of the covering group of the sporadic simple Fischer group F122 and its automorphism group’, Comm. Algebra 22 (1994)35913611.CrossRefGoogle Scholar
13.Hiss, G., Jansen, C., Lux, K. and Parker, R., ‘Computational modular character theory’, 1992, http://www.math.rwth-aachen.de/LDFM/homes/MOC/CoMoChaT/.Google Scholar
14.Huppert, B., Character theory of finite groups (Walter de Gruyter & Co., Berlin, 1998).CrossRefGoogle Scholar
15.Huppert, B. and Blackburn, N., Finite groups II (Springer, Berlin/Heidelberg/New York, 1982).CrossRefGoogle Scholar
16.Jansen, C., Ein Atlas 3-modularer Charaktertafeln, Dissertation, RWTH Aachen, 1995 (Marchal-und Matzenbacher-Wiss.-Verl., Krefeld, 1995).Google Scholar
17.Jansen, C. and Müller, J., ‘The 3-modular decomposition numbers of the sporadic simple Suzuki group’, Comm. Algebra 25 (1997) 24372458.CrossRefGoogle Scholar
18.Jansen, C. and Wilson, R. A., ‘The minimal faithful 3-modular representation for the Lyons group’, Comm. Algebra 24 (1996) 873879.CrossRefGoogle Scholar
19.Jansen, C. and Wilson, R. A., ‘The 2-modular and 3-modular decomposition numbers for the sporadic simple O'Nan group and its triple cover’, J. London Math. Soc. (2) 57(1998) 71–90.CrossRefGoogle Scholar
20.Jansen, C., Lux, K., Parker, R. and Wilson, R., An atlas of Brauer characters (Clarendon Press, Oxford, 1995).Google Scholar
21.Meyer, W., Neutsch, W. and Parker, R., ‘The minimal 5-representation of Lyons sporadic group’, Math. Ann. 272 (1985) 2939.CrossRefGoogle Scholar
22.Müller, J., ‘The 5-modular decomposition matrix of the sporadic simple Conway group C03, Proc. 1998 International Symposium on Symbolic and Algebraic Computation (Rostock) (ACM, New York, 1998) 179185 (electronic).CrossRefGoogle Scholar
23.Müller, J. and Rosenboom, J., ‘Condensation of induced representations and an application: The 2-modular decomposition numbers of C02, Computational methods for representations of groups and algebras (Essen, 1997), Progr. Math. 173 (Birkhäuser, Basel, 1999)309321.Google Scholar
24.Nagao, H. and Tsushima, Y., Representations of finite groups (Academic Press, 1989).Google Scholar
25.Norton, S., ‘On the group Fi24, Geom. Dedicata 25 (1988) 483501.CrossRefGoogle Scholar
26.Ryba, A. J. E., ‘Calculation of the 7-modular characters of the Held group’, J. Algebra 117 (1988)240255.CrossRefGoogle Scholar
27.Suleiman, I. A. I. and Wilson, R. A., ‘The 2-modular characters of Conway's group C02, Math. Proc. Camb. Philos. Soc. 116 (1994) 275283.CrossRefGoogle Scholar
28.Suleiman, I. A. I. and Wilson, R. A., ‘The 2-modular characters of Conway's third group C03, J. Symbolic Comput. 24 (1997) 493506.CrossRefGoogle Scholar
29.Wilson, R. A., ‘A new construction of the Baby Monster and its applications’, Bull. London Math. Soc. 25 (1993) 431437.CrossRefGoogle Scholar
30.Wilson, R. A., et al. , ‘ATLAS of finite group representations’, 2004, http://brauer.maths.qmul.ac.uk/Atlas/.Google Scholar