Finite groups in which maximal subgroups of Sylow p-subgroups are nearly S-permutable

In a group, A is said to satisfy the Np-condition when all subgroups of a Sylow p-subgroup P of A are nearly S-permutable in the normalizer of P in A. If A satisfies the Np-condition for all prime p, then A is called N-group. The objective of this article is to study N-groups. In particular, we explain why every solvable NSPT-group is N-group. We also study groups A in which maximal subgroups of Sylow p-subgroup are nearly S-permutable in the group A. We prove that this class coincides with the class of groups in which maximal subgroups of Sylow p-subgroups are normal in the group A.