Groups whose set of vanishing elements is the union of at most three conjugacy classes. (English) Zbl 1470.20008

Robati, Sajjad Mahmood

Bull. Belg. Math. Soc. - Simon Stevin 26, No. 1, 85-89 (2019).

Summary: 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.

MSC:

20C15	Ordinary representations and characters
20E45	Conjugacy classes for groups

Keywords:

finite groups; vanishing elements; conjugacy classes