2 problems

Let $G$ be a finite group and let $H$ be a finite non-abelian simple group. Write ${\rm Vo}(G)$ for the set of orders of the vanishing elements of $G$, where a vanishing element is…

For a finite group $G$, let $\operatorname{{\mathscr{P}}_{\textit{v}}}(G)$ denote the proportion of elements of $G$ on which some irreducible complex character of $G$ vanishes. Let…