structure of finite groups with trait of non-normal subgroups ii

A finite non-dedekind group g is called an n ac-group if all non-normal abelian subgroups are cyclic. in this paper, all finite n ac-groups will be characterized. also, it will be shown that the center of non-nilpotent n ac- groups is cyclic. if n ac-group g has a non-abelian non-normal sylow subgroup of odd order, then other sylow subgroups of g are cyclic or of quaternion type.