2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126649Let $G$ be a finite group and $V$ be a finite $G$--module. We present upper bounds for the cardinalities of certain subsets of $\Irr(GV)$, such as the set of those $χ\in\Irr(GV)$ such that, for a fixed $v\in V$, the restriction of $χ$ to $<v>$ is not a multiple of the regular character of $<v>$. These results might be useful in attacking the non--coprime $k(GV)$--problem.Representation TheoryGroup Theory20C15text