Question

Question on groups and symmetries

Let G = {(x, y, z): x, y, z are elements on R } and define (x1, y1, z1)*(x2, y2, z2) = (x1+x2, y1+x1z2+y2, z1+z2)

1) Show that (G,*) is a group and that it is non-abelian

2) Show that (G,*) does not have any elements of finite order (other than the identity)