Elementary proof of Brauer's and Nesbitt's theorem on zeros of characters of finite groups

Author:
Manfred Leitz

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3149-3152

MSC (2000):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9939-00-05422-8

Published electronically:
March 3, 2000

MathSciNet review:
1676316

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Abstract | References | Similar Articles | Additional Information

The following has been proven by Brauer and Nesbitt. Let be a finite group, and let be a prime. Assume is an irreducible complex character of such that the order of a -Sylow subgroup of divides the degree of . Then vanishes on all those elements of whose order is divisible by . The two only known proofs of this theorem use profound methods of representation theory, namely the theory of modular representations or Brauer's characterization of generalized characters. The purpose of this paper is to present a more elementary proof.

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Additional Information

**Manfred Leitz**

Affiliation:
Fachbereich Informatik und Mathematik, Fachhochschule Regensburg, Postfach 120327, 93025 Regensburg, Germany

Email:
manfred.leitz@mathematik.fh-regensburg.de

DOI:
https://doi.org/10.1090/S0002-9939-00-05422-8

Received by editor(s):
December 5, 1998

Published electronically:
March 3, 2000

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 2000
American Mathematical Society