## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

#### 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

https://projecteuclid.org/euclid.bbms/1553047230

Digital Object Identifier
doi:10.36045/bbms/1553047230

Mathematical Reviews number (MathSciNet)
MR3934082

Zentralblatt MATH identifier
07060317

#### 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