Centralizers and the maximum size of the pairwise noncommuting elements in finite groups

Authors : Seyyed Majid JAFARİAN AMİRİ, Hojjat ROSTAMİ

Pages : 193-198

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Publication Date : 2017-04-01

Article Type : Research Paper

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 $\omegainsert ignore into journalissuearticles values(G);$ in terms of the order of $G$ where $\omegainsert ignore into journalissuearticles values(G);$ is the maximum size of a set of the pairwise noncommuting elements of $G$.
Keywords : finite group, centralizer, CA group