On Pairs of non-abelian finite p-groups

Let (n,g) be a pair of non-abelian finite p-groups and k be a normal subgroup of g such that g =~ n × k. moreover, let |n| = p^n and |n′| = p^k, where k is a d-generator group of order p^m. then |m(n,g)| = p^½ (n−1)(n−2)+1+(n−1)m−s′ , where m(n,g) is the schur multiplier of the pair (n,g) and s′ is a non-negative integer. in this paper, the non-abelian pairs (n,g) for s′ = 0, 1, 2,3 are characterized.