Let (G,*) be an abelian group. Suppose that there is a surjective group homomorphism 0:(G,*) ({-1,1},-) where is the usual product of real numbers. Consider the binary operation defined on G as follows: alb := a*bla) Va, b E G, where b(a) = b if y(a) 1 and where b(a) = 6-1 is the inverse of b in (G, *) if o(a) = -1. Let e denote the identity of the group (G, *). (i) Show that any subgroup of (G, *) contained in Kero is a normal subgroup of (G, O)