Structure of finite groups with trait of non-normal subgroups II

A finite non-Dedekind group G is called an 𝒩𝒜𝒞-group if all non-normal abelian subgroups are cyclic. In this paper, all finite 𝒩𝒜𝒞-groups will be characterized. Also, it will be shown that the center of non-nilpotent 𝒩𝒜𝒞- groups is cyclic. If 𝒩𝒜𝒞-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.

Keywords:

\NNC-group , \NAC-group , Non-nilpotent groups