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 ‎|N|=p^n and |G/N|=p^m‎. ‎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^{\frac{1}{2}n(2m+n-1)} and hence it is equal to ‎ ‎p^{\frac{1}{2}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\leq 3‎. ‎This paper is devoted to classification of pairs‎ ‎(G,N) when N has a normal complement in G and t=4,5‎.

کلیدواژه های On the order of the schur multiplier of a pair of finite p-groups II:

Pair of groups ، Schur multiplier ، finite p-groups