Classification of groups whose vanishing \\elements are contained in exactly two conjugacy classes

نویسندگان
Mahmood Robati, Sajjad ID 1

1 Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

doi
10.22034/as.2024.20965.1692
چکیده

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 $\chi(g)=0$‎. Moreover, the conjugacy class of a vanishing element is called a vanishing conjugacy class. ‎In this paper‎, ‎we classify groups with exactly two vanishing conjugacy classes and show that such groups are either Frobenius or quasi-Frobenius groups. 

کلیدواژه‌ها
Conjugacy classes, Frobenius groups, Irreducible characters, Solvable groups, Vanishing elements