University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 4 2020 12 01 On n-Nilpotent Groups and n-Nilpotency of n-Abelian Groups 355 366 111284 10.22052/mir.2020.240324.1245 EN Azam Pourmirzaei Department of Mathematics, Hakim Sabzevari University, Sabzevar, I. R. Iran Yaser Shakourie Department of Mathematics, Hakim Sabzevari University, Sabzevar, I. R. Iran Journal Article 2020 10 17 The concept of <em>n</em>-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 <em>n</em>-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 <em>n</em>-nilpotent group <em>G</em> are given based on the assumption that <em>G</em> is <em>n</em>-abelian. nilpotent group n-abelian group n-center subgroup n-potent subgroup https://mir.kashanu.ac.ir/article_111284_8d26176dc2c9950de88884bb0c1ef355.pdf