Hostname: page-component-84b7d79bbc-lrf7s Total loading time: 0 Render date: 2024-07-29T02:21:24.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Prime Power Representations Of Finite Linear Groups

Published online by Cambridge University Press:  20 November 2018

Robert Steinberg
Robert Steinberg*
Affiliation:
Institute for Advanced Study
Rights & Permissions [Opens in a new window]

Extract

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.

1. Introduction. There are five well-known, two-parameter families of simple finite groups: the unimodular projective group, the symplectic group,1 the unitary group,2 and the first and second orthogonal groups, each group acting on a vector space of a finite number of elements (2; 3).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 580 - 591
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Brinckmann, H. W., The group characteristics of the ternary linear fractional group and of various other groups, Bull. Amer. Math. Soc, 27 (1921), 152.Google Scholar
2. Dickson, L. E., Linear groups in Galois fields (Leipzig, 1901).Google Scholar
3. Dieudonné, J., La géométrie des groupes classiques, Ergeb. Math. (Berlin, 1955).Google Scholar
4. Frame, J. S., Some irreducible representations of hyperorthogonal groups, Duke Math. J., 1 (1935), 442–448.Google Scholar
5. Green, J. A., The characters of the finite linear groups, Trans. Amer. Math. Soc, 80 (1955), 402–447.Google Scholar
6. Hartley, R. W., Determination of the ternary collineation groups whose coefficients lie in the GF(2n), Ann. of Math., ser. 2, 29 (1925-26), 140–158.Google Scholar
7. Jordan, H., Group-characters of various types of linear groups, Amer. J. of Math., 29 (1907), 387–405.Google Scholar
8. König, D., Théorie der endlichen und unendlichen Graphen (Chelsea, New York, 1950).Google Scholar
9. Mitchell, H. H., Determination of the ordinary and modular tenary linear groups, Trans. Amer. Math. Soc, 12 (1911), 207–242.Google Scholar
10. Mitchell, H. H., The subgroups of the quaternary abelian linear group, Trans. Amer. Math. Soc, 15 (1914), 379–396.Google Scholar
11. Moore, E. H., The subgroups of the generalized finite modular group, Dec. Publ. Univ. of Chicago, 9 (1904), 141–190.Google Scholar
12. Schur, I., Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. für Math., 182 (1907), 85–137.Google Scholar
13. Steinberg, R., A geometric approach to the representations of the full linear group over a Galois field, Trans. Amer. Math. Soc, 71 (1951), 274–282.Google Scholar
14. Wiman, A., Bestimmung aller Untergruppen einer doppelt unendlichen Reihe von einfachen Gruppen, Handl. Svenska Vet.-Akad., 25 (1899), 1–47.Google Scholar
15. Young, A., On quantitative substitutional analysis (fifth paper), Proc London Math. Soc, ser. 2, 31 (1930), 273–288.Google Scholar