北京邮电大学离散数学群论作业详解
群论9.4 (2)28,32@page 349; 24@page338. 28-Show f:G→G defined by f(a)=a n is a homo morphism.
proof: (数学归纳法证)
1.because ab=ba, ab*ab=aabb=a2b2,
2.(ab)n=a n b n,
ab*(ab)n=ab*a n b n=aa n bb n=a n+1b n+1 Hence, f(ab)=(ab)n=a n b n=f(a)f(b).