Some generalized characters
If \(G\) is a finite group and \(p\) is a prime, define \(\chi_p\colon G\to\mathbb{Z}\) by setting, for \(g\in G\), \[ \chi_p(g)=|\{h\in G\mid\text{the Sylow \(p\)-subgroups of }\langle g,h\rangle\text{ are Abelian}\}|. \] The object of this note is to prove that \(\chi_p\) is a generalized character.
scientific article; zbMATH DE number 868025