Document Type: Research Paper

**Authors**

Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China.

**Abstract**

A $p$-group $G$ is called a $\mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $H\nleq Z(G)$. In this paper, we give a complete classification of finite $\mathcal{CAC}$-$p$-groups.

**Keywords**

**Main Subjects**

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Volume 43, Issue 1

January and February 2017

Pages 171-192

**Receive Date:**25 April 2015**Revise Date:**01 November 2015**Accept Date:**14 February 2017