Okay, I'm really scratching my head here. If an Abelian group A has three generators x,y,z and they are subject to three defining relations, say something like x+y+z=0 x-y-z=0 2x-2y+3z=0 then I can solve for x,y,z and find A as a direct sum of cyclic groups, Z_x + Z_y + Z_z. But what do I do if the three equations are not linearly independent? I get left with everything in terms of x and I can't just plug in the numbers. Thanks, N.