find all homomorphisms of Z3 into Z9 a direct sum ot two cop

find all homomorphisms of Z_3 into Z_9

a direct sum ot two copies of R 5. Find all homomorphisms of Zs into 29.

Solution

In general the number of group homomorphisms :ZmZn is given by gcd(m,n).

i.e If f:GH is a homomorphism, and xG, then the order of f(x) must be a divisor of the order of x.

So here you have gcd(3,9)=3