1. Let : (21)---(3) x (7) be the function defined by the formula:

([x]₂₁):=([x]₃,[x]₇) for xZ

Explain why this function is well-defined, and that it is a homomorphism of groups.

2. Prove the function is injective

3.(3)={1,2}, (7)={1,2,3,4,5,6}, (21)={1,2,4,5,10,11,13,14,16,17,19,20}. So the orders for each of these are 2,6 and 12. Explain why the calculations of orders, together with question 1 and 2, implies that is a bijection, and hence is an isomorphism of group