@article { author = {Wang, J. and Guo, X.}, title = {Finite $p$-groups and centralizers of non-cyclic abelian subgroups}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, number = {1}, pages = {171-192}, year = {2017}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, 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 = {finite $p$-group,centralizer,normal rank,cyclic group}, url = {http://bims.iranjournals.ir/article_1004.html}, eprint = {http://bims.iranjournals.ir/article_1004_cd9f50a94bd9ce4c81bc763dd8930a0a.pdf} }