I am having difficulty solving a problem in Martin Isaac's Character Theory of Finite Groups. Could someone please give me a hint?Thanks in advance!
The problem is as follows:
Let $K$ be T.I.F.N in $G$ and assume that $\mathfrak{J}=\{\psi\in Irr(N(K)):K\nsubseteq ker(\psi)\}$ is coherent. Let $\mathcal{T}$ be the corresponding set of exceptional characters of $G.$ Let $M=\bigcap_{\chi\in\mathcal{T}} ker(\chi).$ Show that $M\cap K=1.$