Finite $p$-groups whose non-central cyclic subgroups have cyclic quotient groups in their centralizers
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 367-376
https://doi.org/10.4134/BKMS.2015.52.2.367
Published online March 31, 2015
Lihua Zhang, Jiao Wang, and Haipeng Qu
Beijing University of Posts and Telecommunications, Shanxi Normal University, Shanxi Normal University
Abstract : In this paper, we classified finite $p$-groups $G$ such that $$C_G(x)/\langle x\rangle$$ is cyclic for all non-central elements $x\in G$. This solved a problem proposed By Y. Berkovoch.
Keywords : centralizers, non-central elements, normal rank, $p$-groups of maximal class
MSC numbers : 20D15
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