A characterization of 4-centralizer groups.
Summary: A finite or infinite group is called an \(n\)-centralizer group if it has \(n\) numbers of distinct centralizers. In this paper, we prove that a finite or infinite group \(G\) is a 4-centralizer group if and only if \(G/Z(G)\) is isomorphic to \(C_2 \times C_2\). This extends a result of \textit{S. M. Belcastro} and \textit{G. J. Sherman} [Math. Mag. 67, No. 5, 366-374 (1994; Zbl 0823.20023)].
scientific article; zbMATH DE number 6356631