Some properties of pair of n-isoclinism induction

Document Type : Research Paper


1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

2 Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran


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.