To find homomorphisms from Z12 to Z13.
Think Z12 is cyclic group of order 12
Let 'a' be the generator of Z12.
Clearly o(a)=12
O(Im(a) )/o(a) i.e. O(I'm(a)) can be 1,2,3,4,6,12.
But Z13 does not have any elements of order 2,3,4,6 and 12 as these numbers does not divide o(Z13)=13.
So O(Im(a)) =1.
This implies 'a' maps to ‘e' identity of Z13.
Which is trivial homomorphism.
Hence only one homomorphism possible.
Number of homomorphism from Zm to Zn is g.c.d(m,n).
Here, g.c.d(12,13)=1
