On zeros of characters of finite groups
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- by David Chillag
- Proc. Amer. Math. Soc. 127 (1999), 977-983
- DOI: https://doi.org/10.1090/S0002-9939-99-04790-5
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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 $G$ is a finite group such that $G\ne G’\ne G''$, then $G$ has an element $x$, such that $|C_G(x)|\le 2m$, where $m$ is the maximal number of zeros in a row of the character table of $G$. 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 $G$ be a finite group such that $1\ne Z(G)\ne Z_2(G)$; then $G$ has an irreducible character $\chi$ such that $\frac {|G|}{\chi ^2(1)}\le 2m$, where $m$ is the maximal number of zeros in a column of the character table of $G$.References
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Bibliographic Information
- David Chillag
- Affiliation: Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
- Email: chillag@techunix.technion.ac.il
- Received by editor(s): August 1, 1997
- Communicated by: Ronald M. Solomon
- © Copyright 1999 American Mathematical Society
- 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
Dedicated: Dedicated to Avinoam Mann on the occasion of his 60th birthday