Document Type : Original Scientific Paper

**Authors**

Department of Mathematics, Hakim Sabzevari University, Sabzevar, I. R. Iran

**Abstract**

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.

**Keywords**

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December 2020

Pages 355-366