On n-Nilpotent Groups and n-Nilpotency of n-Abelian Groups

The concept of n-nilpotent groups was introduced by Moghaddam and Mashayekhy in 1991 which is in a way a generalized version of the notion of nilpotent groups. Using the n-center subgroup, a new series was constructed, which is a generalization of the upper central series of a group. In this article some properties of such groups will be studied. Finally more results for an n-nilpotent group G are given based on the assumption that G is n-abelian.