Normal $p$-complements and irreducible character codegrees
Normal $p$-complements and irreducible character codegrees
Let $G$ be a finite group and $p\in \pi(G)$, and let Irr$(G)$ be the set of all irreducible complex characters of $G$. Let $\chi \in {\rm Irr}(G)$, we write ${\rm cod}(\chi)=|G:{\rm ker} \chi|/\chi(1)$, and called it the codegree of the irreducible character $\chi$. Let $N\unlhd G$, write ${\rm Irr}(G|N)=\{\chi \in …