Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(2): 367-376

Printed March 31, 2015

https://doi.org/10.4134/BKMS.2015.52.2.367

Copyright © The Korean Mathematical Society.

Finite $p$-groups whose non-central cyclic subgroups have cyclic quotient groups in their centralizers

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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