群方程 Proposition 3.6 Let G be a group and a and b be any two elements in G. Then the equations ax=b and xa=b have unique solutions in G. PROOF.Suppose that az=b.We must show that such an z exists. Multiplying both sides of ax=b by a,we have =ex=aa=ab. To show uniqueness,suppose that and2are both solutions of a=b; then ax=b=az2.So 1=aaz1=aax2 =22.The proof for the existence and uniqueness of the solution of a=bis similar. 0 间题5： 直觉上，你能说说群和对称性研究 有什么关联吗？群方程