University of Guilan Journal of Algebra and Related Topics 2345-3931 11 1 2023 06 01 Some properties of pair of n-isoclinism induction 15 26 6246 10.22124/jart.2022.20858.1330 EN M. Sajedi Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran H. Darabi Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran Journal Article 2021 10 18 Let $(G,M)$ be a pair of groups, in which $M$ is a normal subgroup of a group $G.$ We study some properties of $n$-isoclinism of pair of groups. In fact, we show that the subgroups and quotient groups of two $n$-isoclinism pair of groups are $m$-isoclinic for all $m\le n.$ Moreover, the properties of $\pi$-pair and supersolvable pair of groups which are invariant under $n$-isoclinism has be studied. https://jart.guilan.ac.ir/article_6246_71d0d7ed09fe7e40aa63d80e51160bca.pdf