Finite groups with consecutive character codegrees
Xueling Song, Tiantian Shang · International Journal of Algebra · 2025
Let $G$ be a finite group and $\mathrm{Irr}(G)$ be the set of irreducible characters of $G$. The codegree of an irreducible character $\chi$ of the group $G$ is defined as $\mathrm{cod}(\chi)=|G:\mathrm{ker}(\chi)|/\chi(1)$. In this paper, we consider the finite group $G$ whose all irreducible character codegrees are consecutive integers $1,2,3,...,k-1,k$. We prove that $k\leq 3$ and $G$ is an elementary abelian group or a Frobenius group.