University of KashanMathematics Interdisciplinary Research2538-36395420201201On n-Nilpotent Groups and n-Nilpotency of n-Abelian Groups35536611128410.22052/mir.2020.240324.1245ENAzamPourmirzaeiDepartment of Mathematics, Hakim Sabzevari University, Sabzevar, I. R. IranYaserShakourieDepartment of Mathematics,
Hakim Sabzevari University,
Sabzevar, I. R. IranJournal Article20201017The 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.https://mir.kashanu.ac.ir/article_111284_8d26176dc2c9950de88884bb0c1ef355.pdf