Finite $p$-groups and centralizers of non-cyclic abelian subgroups

Document Type : Research Paper


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


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.


Main Subjects

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