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
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.
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.
VANCOUVER
Jafarian Amri, S. M., Amiri, M., Madadi, H., Rostami, H. Finite groups have even more centralizers. Bulletin of the Iranian Mathematical Society, 2015; 41(6): 1423-1431.
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