CHARACTERIZATION OF FINITE p-GROUPS BY THEIR SCHUR MULTIPLIERS

Let G be a finite p-group of order p(n) and M(G) be the Schur multiplier of G. In 1956, Green proved that vertical bar M(G)vertical bar = p((n(n-1)/2)-t(G)), where t(G) >= 0. Berkovich (1991), Zhou (1994) and Ellis (1999) have determined the structure of G, when t(G) = 0, 1,2 and 3, respectively. In 2007, Salemkar et al. classified the structure of G for t(G) = 4 under one condition. In this paper, we characterize all finite abelian p-groups for t(G) >= 0 and non-abelian p-groups, for t(G) = 4 and 5.