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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Inequalities concerning the characters of a finite group


Author: K. L. Fields
Journal: Proc. Amer. Math. Soc. 49 (1975), 289-293
MSC: Primary 20C15
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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0367045-7
PII: S 0002-9939(1975)0367045-7
Keywords: Characters of a finite group, positive semidefinite matrix
Article copyright: © Copyright 1975 American Mathematical Society