Finite2-groups All Of Whose Non-abelian Subgroups Are Self-Centralized

In this paper, we proved that the problem56,736,1484and2487(i) proposed by Berkovich and Janko in their book " Groups of Prime Power Order Ⅰ, Ⅱ, Ⅲ, Ⅳ" are equivalent. Based on the observation, in the case of p=2. the groups in the problem736, finite2-groups G with Cg(H)=Z(H) for all non-abelian subgroups H, are classified using methods of cyclic extension.