Abstract
For any finite solvable group G we show that if three primes dividing the degrees of certain irreducible characters of G are given, then there exists an irreducible character of G with degree divisible by at least two of the given primes.
Similar content being viewed by others
REFERENCES
D. Gorenstein, Finite Groups, Harper & Row, New York-Evanston-London, 1968. (MR 38#229)
B. Huppert, Endliche Gruppen, I, Springer, Berlin-Heidelberg-New York, 1967. (MR 37#302)
B. Huppert, O. Manz, Degree-problems I: Squarefree character degrees, Arch. Math. 45 (1985), 125-132. (MR 87i:20015)
I. M. Isaacs, Character theory of finite groups, Academic Press, San Diego, 1976. (MR 57#417)
O. Manz, Endliche auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind J. Algebra, 94 (1985), 211-255. (MR 87c:20022)
O. Manz, Degree problems II: π-separable character degrees Commun. Algebra 13 (1985), 2421-2431. (MR 86m:20009)
O. Manz, W. Willems and T. R. Wolf, The diameter of the character degree graph J. reine angew. Math. 402 (1989), 181-198. (MR 90i:20007)
O. Manz, T. R. Wolf, Representations of Solvable Groups, London Math. Soc. Lecture Notes Ser. vol. 185, Cambridge Univ. Press, 1993. (MR 95c:20013)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pálfy, P.P. On the Character Degree Graph of Solvable Groups, I Three Primes. Periodica Mathematica Hungarica 36, 61–65 (1998). https://doi.org/10.1023/A:1004659919371
Issue Date:
DOI: https://doi.org/10.1023/A:1004659919371