- Hacettepe Journal of Mathematics and Statistics
- Vol: 46 Issue: 2
- Centralizers and the maximum size of the pairwise noncommuting elements in finite groups
Centralizers and the maximum size of the pairwise noncommuting elements in finite groups
Authors : Seyyed Majid Jafarian Amiri, Hojjat Rostami
Pages : 193-198
View : 12 | Download : 7
Publication Date : 2017-04-01
Article Type : Research
Abstract :In this article, we determine the structure of all nonabelian groups $G$ such that $G$ has the minimum number of the element centralizers among nonabelian groups of the same order. As an application of this result, we obtain the sharp lower bound for $\omega(G)$ in terms of the order of $G$ where $\omega(G)$ is the maximum size of a set of the pairwise noncommuting elements of $G$.Keywords : finite group, centralizer, CA-group