[SOLVED] group theory

ehrenfest

1. The problem statement, all variables and given/known data
My book says that Z_3 cross Z_4 is isomorphic to Z_12, which I am confused about because
Z_3 cross Z_4 has four different generators and Z_12 only has 1.

EDIT: wait that is not true, Z_12 has generators 1,5,7,11
It is probably true in general that the number of generators of Z_n is equal to phi(n) where phi is the Euler phi function.
2. Relevant equations



3. The attempt at a solution