Finite groups in which different conjugacy classes have different cardinalities
This note contains an elementary proof of the following result of \textit{J. P. Zhang} [J. Algebra 170, No. 2, 608-624 (1994; Zbl 0816.20023)]: if \(G\) is a finite nonabelian group in which distinct conjugacy classes of noncentral elements have different cardinalities, then \(Z(G)=1\).
scientific article; zbMATH DE number 883760