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Projective Representations of Minimum Degree of Group Extensions

Published online by Cambridge University Press:  20 November 2018

Walter Feit
Affiliation:
Institut des Hautes Etudes Scientifiques, Bures sur Yvette, France
Jacques Tits
Affiliation:
Institut des Hautes Etudes Scientifiques, Bures sur Yvette, France
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Let G be a finite simple group and let F be an algebraically closed field. A faithful projective F-representation of G of smallest possible degree often cannot be lifted to an ordinary representation of G, though it can of course be lifted to an ordinary representation of some central extension of G. It is a natural question to ask whether by considering non-central extensions, it is possible in some cases to decrease the smallest degree of a faithful projective representation.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Feit, W., The current situation in the theory of finite simple groups, Actes du Congres International des Mathématiciens, Nice (1970), Vol. 1, 5593.Google Scholar
2. Griess, R. L., Jr., Automorphisms of extra special groups and nonvanishing degree 2 cohomology, Pacific J. Math. 48 (1973), 403422.Google Scholar
3. Huppert, B., Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenshaften, Band 134 (Springer-Verlag, Berlin-New York, 1967).Google Scholar
4. Landazuri, V. and Seitz, G. M., On the minimal degrees of projective representations of the finite Chevalley groups, J. Algebra 32 (1974), 418443.Google Scholar
5. Lindsey, J. H., II, Finite linear groups of degree six, Can. J. Math. 23 (1971), 771790.Google Scholar
6. Tits, J., Groupes simples et geometries associées, Proc. Int. Cong. Math. Stockholm, Stockholm (1962), 197221.Google Scholar