SOME PROPERTIES OF PAIR OF n-ISOCLINISM INDUCTION.

Let (G;M) be a pair of groups, in whichM 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 ≤ n: Moreover, the properties of π-pair and supersolvable pair of groups which are invariant under n-isoclinism has be studied. [ABSTRACT FROM AUTHOR]