Jiang Min PAN
Let Sri(i=1,2,…,n) be free metabelian groups of rank ri,G = Sr1×Sr2×…×Srn be direct product of free metabelian groups. In this paper, we prove that G has test element if and only if ri=2 (i = 1,2,…,n). Meanwhile, we prove that 3 = (g1,g2,…,gn) is a test element of G if and only if gi∈S'2 - 1 (i = 1,2,…,n), and {g1,g2,…,gn} is an independent set.