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On the heights of group characters


Author: R. J. Haggarty
Journal: Proc. Amer. Math. Soc. 63 (1977), 213-216
MSC: Primary 20C20
DOI: https://doi.org/10.1090/S0002-9939-1977-0435199-1
MathSciNet review: 0435199
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Abstract: For a finite p-soluble group G we derive a bound on the heights of the irreducible complex characters of G lying in a p-block B. This bound depends on the prime p and the exponent d of a defect group of B. We show by examples that this bound is of the right order of magnitude.


References [Enhancements On Off] (What's this?)

  • [1] R. Brauer, Some applications of the theory of blocks of characters of finite groups. IV, J. Algebra 17 (1971), 489-521. MR 43 #7520. MR 0281806 (43:7520)
  • [2] R. Brauer and W. Feit, On the number of irreducible characters of finite groups in a given block, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 361-365. MR 0106246 (21:4980)
  • [3] P. Fong, Some properties of characters of finite solvable groups, Bull. Amer. Math. Soc. 66 (1960), 116-117. MR 22 #2655. MR 0111794 (22:2655)
  • [4] -, On the characters of p-solvable groups, Trans. Amer. Math. Soc. 98 (1961), 263-284. MR 22 #11052. MR 0120297 (22:11052)
  • [5] P. Hall and G. Higman, On the p-length of p-soluble groups and reduction theorems for Burnside's problem, Proc. London Math. Soc. (3) 6 (1956), 1-42. MR 17, 344. MR 0072872 (17:344b)
  • [6] B. Huppert, Endliche Gruppen. I, Die Grundlehren der math. Wissenschaften, Band 134, Springer-Verlag, Berlin and New York, 1967. MR 37 #302. MR 0224703 (37:302)
  • [7] -, Linear auflösbare Gruppen, Math. Z. 67 (1957), 479-518. MR 19, 729.
  • [8] D. L. Winter, p-solvable linear groups of finite order, Trans. Amer. Math. Soc. 157 (1971), 155-160. MR 43 #2092. MR 0276345 (43:2092)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0435199-1
Keywords: Modular representations, block, defect, height
Article copyright: © Copyright 1977 American Mathematical Society

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