1) How many distinct homomorphisms phi:C_3 ---> C_12 are there? How many of these are injective?
2) How many distinct homomorphisms phi:C_91 ---> C_1001 are there? How many of these are injective?
C_n means that of the numbers coprime to n at least one of them (say m) generates the group of coprime numbers mod n where the group is {1, m, m^2,......., m^n-1}.
we know that if there is a homomoprhism f, from group G to H, then if the order of g equals n then the order of f(g)|n
Thanks