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On projective characters of the same degree

Published online by Cambridge University Press:  18 May 2009

R. J. Higgs
R. J. Higgs
Affiliation:
Department of Mathematics, University College, Dublin, Ireland
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All groups G considered in this paper are finite and all representations of G are defined over the field of complex numbers. The reader unfamiliar with projective representations is referred to [9] for basic definitions and elementary results. Let Proj (G, α) denote the set of irreducible projective characters of a group G with cocyle α. In previous papers (for exampe [2], [4], and [6]) numerous authors have considered the situation when Proj(G, α) = 1 or 2; such groups are said to be of α-central type or of 2α-central type, respectively. In particular in [4, Theorem A] the author showed that if Proj(G, α) = {ξ1, ξ2}, then ξ1(1)=ξ2(1). This result has recently been independently confirmed in [8, Corollary C].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 431 - 434
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Conway, J. H. et al. , An atlas of finite groups (Oxford University Press, 1985).Google Scholar
2.DeMeyer, F. R. and Janusz, G. J., Finite groups with an irreducible representation of large degree, Math. Z. 108 (1969), 145–153.CrossRefGoogle Scholar
3.Feit, W. and Seitz, G. M., On finite rational groups and related topics, Illinois J. Math. 33 (1988), 103–131.Google Scholar
4.Higgs, R. J., Groups with two projective characters, Math. Proc. Camb. Phil. Soc. 103 (1988), 5–14.CrossRefGoogle Scholar
5.Higgs, R. J., Projective characters of degree one and the inflation–restriction sequence, J. Austral. Math. Soc. (Series A) 46 (1989), 272–280.CrossRefGoogle Scholar
6.Howlett, R. B. and Isaacs, I. M., On groups of central type, Math. Z. 179 (1982), 555–569.CrossRefGoogle Scholar
7.Isaacs, I. M., Character correspondences in solvable groups, Advancesin Math. 43 (1982), 284–306.CrossRefGoogle Scholar
8.Isaacs, I. M., Blocks with just two irreducible Brauer characters in solvable groups, J. Algebra 170 (1994), 487–503.CrossRefGoogle Scholar
9.Karpilovsky, G., Projective representations of finite groups, Monographs and Textbooks in Pure and Applied Mathematics 94. (Marcel Dekker, 1985).Google Scholar
10.Liebler, R. A. and Yellen, J. E., In search of nonsolvable groups of central type, Pacific J. Math. 82 (1979), 485–492.CrossRefGoogle Scholar
11.Ng, N. G., Degrees of irreducible projective representations of finite groups, J. London Math. Soc. (2) 10 (1975), 379–384.CrossRefGoogle Scholar