ON THE ORDER OF THE SCHUR MULTIPLIER OF A PAIR OF FINITE p-GROUPS II

Let G be a FInite p-group and N be a normal subgroup of G with jNj = pn and jG=Nj = pm. A result of Ellis (1998) shows that the order of the Schur multiplier of such a pair (G;N) of FInite p- groups is bounded by p 1 2 n(2m+n-1) and hence it is equal to p 12 n(2m+n-1)-t for some non-negative integer t. Recently, the authors have characterized the structure of (G;N) when N has a complement in G and t 3. This paper is devoted to classification of pairs (G;N) when N has a normal complement in G and t = 4; 5.