1. prove

Prove that there is no homomorphism from Z_8 (+) Z_2 onto Z_4 (+) Z_4

[(+) is the external direct product]

2. Originally Posted by mandy123
Prove that there is no homomorphism from Z_8 (+) Z_2 onto Z_4 (+) Z_4

[(+) is the external direct product]

Hint: Any homomorphism is determined by $f( 1,1)$.
Try to arrive to a contradiction.