Sharp characters of finite groups of type \(\{-1,1\}\)
It is known that \(|{\mathcal G}|\) divides \(\prod_{t\in T} (n-t)\), where \(n=\chi(1)\), \(\chi\) a virtual character of the finite group \({\mathcal G}\), \(T=\{\chi(g)\); \(g\in{\mathcal G}\setminus\{1\}\}\). This is a result proved by Blichfeldt, Cameron and Kiyota, Hekster. Note that indeed \(\prod_{t\in T} (n-t)\in\mathbb{Z}\). If \(|{\mathcal G}|=\prod_{t\in T} (n-t)\), then we say that \(\chi\) is sharp of type \(T\). In this paper the groups \({\mathcal G}\) are determined admitting \(\chi\in \text{char}({\mathcal G})\) that are sharp of type \(\{-1,+1\}\).
scientific article; zbMATH DE number 130498