群方程和消去律 Proposition 3.21.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 a.x=b.We must show that such an r exists.We can multiply both sides of ax b by a-1 to find x ex=a-lax =a-1b. To show uniqueness,suppose that xi and r2 are both solutions of ax=b;then ari b=ax2.So 1 a-ax1 a-ax2 22.The proof for the existence and uniqueness of the solution of xa =b is similar. 口 Proposition 3.22.If G is a group and a,b,cEG,then ba ca implies b=c and ab=ac implies b =c. 间题4： 直觉上，你能说说群和对称性研究有什么关联吗？群方程和消去律