On the order of Schur multipliers of finite Abelian p-groups

Abstract

Let G be a finite p-group of order p n with |M(G)| = p n(n�1) 2 −t , where M(G) is the Schur multiplier of G. Ya.G. Berkovich, X. Zhou, and G. Ellis have determined the structure of G when t =0 ,1,2,3. In this paper, we are going to find some structures for an abelian p-group G with conditions on the exponents of G,M(G), and S2M(G), where S2M(G) is the metabelian multiplier of G. Mathematics Subject Classification: 20C25; 20D15; 20E34; 20E10