Bulletin of the Belgian Mathematical Society - Simon Stevin

Groups whose set of vanishing elements is the union of at most three conjugacy classes

Sajjad Mahmood Robati

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Abstract

Let $G$ be a finite group. We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $\chi$ of $G$ such that $\chi(g)=0$. In this paper, we prove that if the set of vanishing elements of $G$ is the union of at most three conjugacy classes, then $G$ is solvable.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 1 (2019), 85-89.

Dates
First available in Project Euclid: 20 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1553047230

Digital Object Identifier
doi:10.36045/bbms/1553047230

Mathematical Reviews number (MathSciNet)
MR3934082

Zentralblatt MATH identifier
07060317

Subjects
Primary: 20C15: Ordinary representations and characters 20E45: Conjugacy classes

Keywords
Finite groups vanishing elements conjugacy classes

Citation

Robati, Sajjad Mahmood. Groups whose set of vanishing elements is the union of at most three conjugacy classes. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 1, 85--89. doi:10.36045/bbms/1553047230. https://projecteuclid.org/euclid.bbms/1553047230


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