Groups whose set of vanishing elements is exactly a conjugacy class

Document Type : Research Paper

Author

‎Department of mathematics‎, ‎Faculty of Science, Imam Khomeini International University, Qazvin‎, ‎Iran.

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 classify groups whose set of vanishing elements is exactly a conjugacy class‎.

Keywords

References

[1] S. Dol , E. Paci ci, L. Sanus, and P. Spiga, On the vanishing prime graph of solvable groups, J. Group
Theory, Vol. 13 No. 2 (2010), pp. 189-206.
[2] L. Dornho , Group representation theory. Part A: Ordinary representation theory, Marcel Dekker, New
York, (1971).
[3] I. M. Isaacs, Character theory of nite groups, New York-San Francisco-London: Academic Press, (1976).
[4] I. M. Isaacs, G. Navarro, and T. R. Wolf, Finite group elements where no irreducible character vanishes,
J. Algebra, Vol. 222 No. 2 (1999), pp. 413-423.
[5] S. M. Robati, Groups whose set of vanishing elements is the union of at most three conjugacy classes, Bull. Belg. Math. Soc. Simon Stevin, Vol. 26 No. 1 (2019), pp. 85-89.
 
Algebraic Structures and Their Applications
Volume 6, Issue 2
November 2019
Pages 9-12

Files

Share

How to cite

Statistics