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

چکیده مقاله

In this paper, we investigate the finite groups all of whose non-normal nilpotent subgroups are cyclic. We show that such groups are solvable with cyclic centers. If G is a non-supersolvable group, then G has only one noncyclic Sylow subgroup which is either isomorphic to Q8 or is of type (q, q).