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Groups whose Projective character degrees are powers of a prime†

Published online by Cambridge University Press:  18 May 2009

R. J. Higgs
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Let Gbe a finite group, and P:G → GL(n, ) be such that for all x, y ∈ G

(i) P(x)P(y) = α(x, y)P(xy), and

(ii)P(l) = In,

where α(x, y) ∈ *; then P is a projective representation of G with cocycle α and degree n. For other basic definitions concerning projective representations see [4].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 2 , May 1988 , pp. 177 - 180
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Glauberman, G., The revision project and pushing-up, pp. 207–223 in: Finite simple groups II (Academic Press, 1980).Google Scholar
2.Gluck, D. and Wolf, T. R., Defect groups and character heights in blocks of solvable groups II, J. Algebra 87, (1984), 222–246.CrossRefGoogle Scholar
3.Gorenstein, D., Finite groups, (Harper and Row, 1968).Google Scholar
4.Haggarty, R. J. and Humphreys, J. F., Projective characters of finite groups, Proc. London Math. Soc. (3) 36 (1978), 176–192.CrossRefGoogle Scholar
5.Isaacs, I. M. and Passman, D. S., Groups whose irreducible representations have degrees dividing p e, Illinois J. Math. 8 (1964), 446–457.CrossRefGoogle Scholar