北京邮电大学 离散数学下 群论 作业错题讲解(7)

北京邮电大学离散数学群论作业详解

群论9.1-9.2 Ex2: Let G be a group, and suppose that a and b are any elements of G.

Show that if (ab)2=a2b2,,then ba=ab.

proof:

(ab)2=ab*ab=a*(b*a)*b

a2b2=aa*bb=a*(a*b)*b,

based left/right cancellation, b*a=a*b.