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.
4.Griess JR, R. L., and Smith, S. D., ‘Minimal dimensions for modular representations of the Monster’, Comm. Algebra 22 (1994) 6279–6294.CrossRefGoogle Scholar
5
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) 58–70.CrossRefGoogle Scholar
6
6.Hensing, S., ‘5-modulare Zerlegungszahlen der sporadischen einfachen Gruppe C01 und ihrer Überlagerungsgruppe 2.C01’, Diplomarbeit, Universität Heidelberg, 1993.Google Scholar
7
7.Hiss, G., ‘The 3-modular characters of the Rudvalis group and its covering group’, Math. Comput. 62 (1994) 851–863.CrossRefGoogle Scholar
8
8.Hiss, G., ‘Decomposition matrices of the Chevalley group F4(2) and its covering group’, Comm. Algebra25 (1997) 2539–2555.CrossRefGoogle Scholar
9
9.Hiss, G. and Lux, K., Brauer trees of sporadic groups (Clarendon Press, Oxford, 1989).Google Scholar
10
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. Algebra22 (1994) 3563–3590.Google Scholar
11
11.Hiss, G. and Müller, J., ‘The 5-modular characters of the sporadic simple Rudvalis group and its covering group’, Comm. Algebra23 (1995) 4633–667.CrossRefGoogle Scholar
12
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. Algebra22 (1994)3591–3611.CrossRefGoogle Scholar
17.Jansen, C. and Müller, J., ‘The 3-modular decomposition numbers of the sporadic simple Suzuki group’, Comm. Algebra25 (1997) 2437–2458.CrossRefGoogle Scholar
18
18.Jansen, C. and Wilson, R. A., ‘The minimal faithful 3-modular representation for the Lyons group’, Comm. Algebra24 (1996) 873–879.CrossRefGoogle Scholar
19
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
20.Jansen, C., Lux, K., Parker, R. and Wilson, R., An atlas of Brauer characters (Clarendon Press, Oxford, 1995).Google Scholar
21
21.Meyer, W., Neutsch, W. and Parker, R., ‘The minimal 5-representation of Lyons sporadic group’, Math. Ann.272 (1985) 29–39.CrossRefGoogle Scholar
22
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) 179–185 (electronic).CrossRefGoogle Scholar
23
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)309–321.Google Scholar
24
24.Nagao, H. and Tsushima, Y., Representations of finite groups (Academic Press, 1989).Google Scholar
25
25.Norton, S., ‘On the group Fi24’, Geom. Dedicata25 (1988) 483–501.CrossRefGoogle Scholar
26
26.Ryba, A. J. E., ‘Calculation of the 7-modular characters of the Held group’, J. Algebra117 (1988)240–255.CrossRefGoogle Scholar
27
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) 275–283.CrossRefGoogle Scholar
28
28.Suleiman, I. A. I. and Wilson, R. A., ‘The 2-modular characters of Conway's third group C03’, J. Symbolic Comput.24 (1997) 493–506.CrossRefGoogle Scholar
29
29.Wilson, R. A., ‘A new construction of the Baby Monster and its applications’, Bull. London Math. Soc.25 (1993) 431–437.CrossRefGoogle Scholar