CLASSIFYING p-GROUPS BY THEIR SCHUR MULTIPLIERS

Some recent results devoted to the investigation of the structure of p-groups rely on the study of their Schur multipliers. One of these results states that for any p-group G of order p(n) there exists a nonnegative integer s(G) such that the order of the Schur multiplier of G is equal to p(1/2(n-1)(n-2)+1-s(G)). Characterizations of the structure of all non-abelian p-groups G have been obtained for the case that s(G) = 0 or 1. The present paper is devoted to the characterization of all p-groups with s(G) = 2.