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Inequalities concerning the characters of a finite group


Author: K. L. Fields
Journal: Proc. Amer. Math. Soc. 49 (1975), 289-293
MSC: Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-1975-0367045-7
Erratum: Proc. Amer. Math. Soc. 61 (1976), 186.
MathSciNet review: 0367045
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Abstract: Given a finite group we provide explicit bounds (in terms of the group order and numbers of conjugacy classes and involutions) for (a) the number of real valued characters of type $ {\mathbf{R}}$; (b) the sum of the degrees of the irreducible characters; (c) the sum of the entries of the character table; (d) the sums (b), (c) restricted to real valued characters. We also provide a bound on the number of elements of order $ 2n$ in terms of the number of elements of order $ n$.


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

  • [1] R. Brauer, Representations of finite groups, Lectures on Modern Mathematics, vol. 1, Wiley, New York, 1963, pp. 133-175 (Problem 14). MR 31 #2314. MR 0178056 (31:2314)
  • [2] R. Brauer and K. A. Fowler, On groups of even order, Ann. of Math. (2) 62 (1955), 565-583. MR 17, 580. MR 0074414 (17:580e)
  • [3] K. L. Fields, On the conjugating representation of a finite group, Proc. Amer. Math. Soc. 34 (1972), 35-37. MR 45 #6941. MR 0297889 (45:6941)
  • [4] G. Frobenius and I. Schur, Über die Reellen Darstellungen der endlichen Gruppen, S.-B. Preuss. Akad. Wiss. 1906, 186-208.
  • [5] L. Solomon, On the sum of the elements in the character table of a finite group, Proc. Amer. Math. Soc. 12 (1961), 962-963. MR 24 #A2619. MR 0132783 (24:A2619)

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DOI: https://doi.org/10.1090/S0002-9939-1975-0367045-7
Keywords: Characters of a finite group, positive semidefinite matrix
Article copyright: © Copyright 1975 American Mathematical Society

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