let $g$ be a finite group and let $n$ be a normal subgroup of $g$. suppose that ${rm{irr}} (g | n)$ is the set of the irreducible characters of $g$ that contain $n$ in their kernels. in this paper, we classify solvable groups $g$ in which the set $mathcal{c} (g) = {{rm{irr}} (g | n) | 1 ne n trianglelefteq g }$ has at most three elements. we also compute the set $mathcal{c}(g)$ for suc...
