Author/Authors :
Jafarian Amiri، Seyyed Majid نويسنده Department of Mathematics, Faculty of Sciences, University of Zanjan , , Amiri، Mohsen نويسنده Department of Mathematics, Faculty of Sciences, University of Zanjan , , Madadi، Halimeh نويسنده Department of Mathematics, Faculty of Sciences, University of Zanjan , , Rostami، Hojjat نويسنده Department of Mathematics, Faculty of Sciences, University of Zanjan ,
Abstract :
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|\leq \frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $G\cong S_3, D_{10}$ or $S_3\times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, {\em Algebra
Colloq.} {7} (2000), no. 2, 139--146].
