Geodesic
On projective characters of prime degree
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 311-321

Voir la notice de l'article provenant de la source Cambridge University Press

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 cocycle α. In a previous paper [3] the author showed that if G is a (p, α)-group, that is the degrees of the elements of Proj(G, α) are all powers of a prime number p, then G is solvable. However Isaacs and Passman in [8] were able to give structural information about a group G for which ξ(1) divides pe for all ξ ∈ Proj(G, 1), where 1 denotes the trivial cocycle of G, and indeed classified all such groups in the case e = l. Their results rely on the fact that G has a normal abelian p-complement, which is false in general if G is a (p, α)-group; the alternating group A4 providing an easy counter-example for p = 2. 
Higgs, R. J. On projective characters of prime degree. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 311-321. doi: 10.1017/S0017089500008387
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[1] 1.DeMeyer, F. R. and Janusz, G. J., Finite groups with an irreducible representation of large degree. Math. Z. 108 (1969), 145–153. Google Scholar | DOI

[2] 2.Higgs, R. J., On the degrees of projective representations. Glasgow Math. J. 30 (1988), 133–135. Google Scholar | DOI

[3] 3.Higgs, R. J., Groups whose projective character degrees are powers of a prime. Glasgow Math. J. 30 (1988), 177–180. Google Scholar | DOI

[4] 4.Higgs, R. J., Projective characters of degree one and the inflation-restriction sequence. J. Austral. Math Soc. (Series A) 46 (1989), 272–280. Google Scholar | DOI

[5] 5.Hoffman, P. N. and Humphreys, J. F., Non-isomorphic groups with the same projective character tables. Comm. Algebra 15 (1987), 1637–1648. Google Scholar | DOI

[6] 6.Huppert, B., Endliche Gruppen. I. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 134, (Springer-Verlag, Berlin, Heidelberg, New York, 1967). Google Scholar | DOI

[7] 7.Isaacs, I. M., Character theory of finite groups. (Pure and Applied Mathematics, a series of monographs and textbooks; 69), (Academic Press, New York, London, 1976). Google Scholar

[8] 8.Isaacs, I. M. and Passman, D. S., Groups whose irreducible representations have degrees dividing pe. Illinois J. Math. 8 (1964), 446–457. Google Scholar | DOI

[9] 9.Karpilovsky, G., Projective representations of finite groups. (Monographs and Textbooks in Pure and Applied Mathematics; 94), (Marcel Dekker, New York, Basel, 1985). Google Scholar

[10] 10.Karpilovsky, G., The Schur multiplier. (London Mathematical Society monographs; new ser., 2), (Oxford University Press, Oxford, New York, 1987). Google Scholar

[11] 11.Ng, H. N., Degrees of irreducible projective representations of finite groups. J. London Math. Soc. (2) 10 (1975), 379–384. Google Scholar | DOI

[12] 12.Read, E. W., On the centre of a representation group. J. London Math. Soc. (2) 16 (1977), 43–50. Google Scholar | DOI

[13] 13.Tahara, K. I., On the second cohomology groups of semidirect products. Math Z. 129 (1972), 365–379. Google Scholar | DOI

[14] 14.Thomas, A. D. and Wood, G. V., Group tables. (Shiva mathematics series; 2), (Shiva, Orpington, 1980). Google Scholar

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