21.108 (2026)

For a finite group $G$ let $\text{Cod}(G)$ denote the set of irreducible character codegrees of $G$ (see 20.78). Define $\sigma(G) = \max\{|\pi(m)|: m \in \text{Cod}(G)\}$, where $\pi(m)$ denotes the set of prime divisors of an integer $m$. It is proved that there exists a constant $k$ such that $|\pi(G)| \leqslant k \cdot \sigma(G)$ for every finite group $G$ (Y. Yang, G. Qian, J. Algebra, 478 (2017), 215–219), but the estimate provided for $k$ is very crude. Can the constant $k$ be taken as 4?