Some properties of pair of n-isoclinism induction

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.

Keywords:

Pair of groups , n-isoclinism , Supersolvable pair , \pi-seperable