1. It is proved that the corresponding relation of (4-2-2) is isomorphic.

It is proved that let G={a 1, a2, …, an}, and specify any element ai in G, any aj∈G, Pi: AJ → AJAI, then Pi is a permutation on G, that is, take G as the target set. Pi=，

Right regular representation of g f: ai → = pi. F is injective: ai≠aj, then Pi≠Pj.

f(aiaj)= = =f(ai)f(aj)

Complete the certificate.

2. It is proved that for any element A of finite group G, there exists an integer R, which makes AR = E, and R is divisible by G, which is the order of group G. ..

Certificate: Let |G|=g, then there must be the same elements in A, a2, a3, …, ag, ag+ 1. ak=al， 1≤k