### Groups and Uniqueness of Decompositions

Let A = Z + Z + Z, let x_1 = (1,2,1) and x_2 = (1,5,1), and consider the subgroup B = (x_1, x_2) is a member of G. For the quotient group G = A/B, and write (x,y,z) is a member of G for the coset determined by n element (x,y,z) is a member of A. a) For the subgroups J_1 = {x,y,0 for | x,y is a member of Z} and J_2 = {(0,0,z)