The characterization of PSL(2, p) (p≡±5 (mod 24))

Abstract

Let G be a finite group. A vanishing element of G is an element $g\in G$ such that $\chi (g)=0$ for some irreducible complex character χ of G. We will denote by Van(G) the set of vanishing elements of G and by $\text{Vo}(G)$ the set of the order of elements in $\text{Van}(G)$. For certain specified primes p that satisfy $p\equiv \pm 5\hspace{1em}(\mathrm{\text{mod}}24)$, if $\text{Vo}(G)=\text{Vo}(\text{PSL}(2,p))$, then $G\cong \text{PSL}(2,p)$.

KEYWORDS:

• Characters
• finite simple groups
• vanishing elements

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20C15

Acknowledgments

The first author wishes to express his gratefulness to Dr Baoyu Zhang. The authors wish to express their gratefulness to the referee.

Data availability statement

The authors declare that data supporting the findings of this study are available within the article.

Disclosure statement

The authors declare no conflicts of interest.

Additional information

Funding

The work is supported in part by the Natural Science Foundation of China (No. 12071181).