Zeros of irreducible characters lying in a normal subgroup

M. J. Felipe, N. Grittini, V. M. Ortiz-Sotomayor

Published 2019-02-08Version 1

Let $N$ be a normal subgroup of a finite group $G$. An element $g\in G$ such that $\chi(g)=0$ for some irreducible character $\chi$ of $G$ is called a vanishing element of $G$. The aim of this paper is to analyse the influence of the $\pi$-elements in $N$ which are (non-)vanishing in $G$ on the $\pi$-structure of $N$, for a set of primes $\pi$. In particular, we also study certain arithmetical properties of their $G$-conjugacy class sizes.