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 exists. Multiplying both sides of ax =b by a,we have =ex=a-ax=a-b. To show uniqueness,suppose that and are both solutions of ab; then a =b=az2.So 21=aaz aaz2 22.The proof for the existence and uniqueness of the solution of a =b is similar. 0 间题8： 直觉上，你能说说群和对称性研究 有什么关联吗？群方程