Department of Mathematics, Faculty of Sciences, University of Zanjan, P.O. Box 45371-38791, Zanjan, Iran
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, Algebra Colloq. 7 (2000), no. 2, 139--146].
Jafarian Amri, S. M., Amiri, M., Madadi, H., & Rostami, H. (2015). Finite groups have even more centralizers. Bulletin of the Iranian Mathematical Society, 41(6), 1423-1431.
MLA
Jafarian Amri, S. M., Amiri, M., Madadi, H., & Rostami, H. "Finite groups have even more centralizers", Bulletin of the Iranian Mathematical Society, 41, 6, 2015, 1423-1431.
HARVARD
Jafarian Amri S. M., Amiri M., Madadi H., Rostami H. (2015). 'Finite groups have even more centralizers', Bulletin of the Iranian Mathematical Society, 41(6), pp. 1423-1431.
CHICAGO
S. M. Jafarian Amri, M. Amiri, H. Madadi & H. Rostami, "Finite groups have even more centralizers," Bulletin of the Iranian Mathematical Society, 41 6 (2015): 1423-1431,
VANCOUVER
Jafarian Amri S. M., Amiri M., Madadi H., Rostami H. Finite groups have even more centralizers. BIMS. 2015;41(6):1423-1431.
