On zeros of characters of finite groups

Author:
David Chillag

Journal:
Proc. Amer. Math. Soc. **127** (1999), 977-983

MSC (1991):
Primary 20Cxx

DOI:
https://doi.org/10.1090/S0002-9939-99-04790-5

MathSciNet review:
1487363

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Abstract: We present several results connecting the number of conjugacy classes of a finite group on which an irreducible character vanishes, and the size of some centralizer of an element. For example, we show that if is a finite group such that , then has an element , such that , where is the maximal number of zeros in a row of the character table of . Dual results connecting the number of irreducible characters which are zero on a fixed conjugacy class, and the degree of some irreducible character, are included too. For example, the dual of the above result is the following: Let be a finite group such that ; then has an irreducible character such that , where is the maximal number of zeros in a column of the character table of .

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Additional Information

**David Chillag**

Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

Email:
chillag@techunix.technion.ac.il

DOI:
https://doi.org/10.1090/S0002-9939-99-04790-5

Received by editor(s):
August 1, 1997

Dedicated:
Dedicated to Avinoam Mann on the occasion of his 60th birthday

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1999
American Mathematical Society