Zeros of irreducible characters in factorised groups

M. J. Felipe; A. Martínez-Pastor; V. M. Ortiz-Sotomayor

doi:10.1007/s10231-018-0765-5

paper

Zeros of irreducible characters in factorised groups

arXiv:1803.00432 · doi:10.1007/s10231-018-0765-5

Abstract

An element $g$ of a finite group $G$ is said to be vanishing in $G$ if there exists an irreducible character $χ$ of $G$ such that $χ (g) = 0$ ; in this case, $g$ is also called a zero of $G$ . The aim of this paper is to obtain structural properties of a factorised group $G = A B$ when we impose some conditions on prime power order elements $g \in A \cup B$ which are (non-)vanishing in $G$ .