一类具有特殊中心化子的有限p-群

On a Class of p-Groups with Special Centralizers

若一个非交换的有限p-群G的任意非交换子群H满足CG(H)=Z(H),则称G为CGZ-群.主要研究了幂零类是2的CGZ-群G,证明了Ω1(G)≤Z(G)以及d(G)≤3.

A finite p-group G is called a CGZ-group if and only if every non-abelian subgroup H of G satis-fying CG（H）= Z（H） .In this paper ,it is proved that ,if G be a finite p-group with cl（G）=2 ,and if G is a CGZ-group ,then 1Ω（G）≤ Z（G） and d（G）≤3 .