# Group homomorphisms functions

Homomorphism

Problem 4:

Let G, G1, and G2 be groups. Let µ1 : G -> G1 and µ2 : G -> G2 be group homomorphisms. Prove that

µ : G -> G1 × G2 defined by :

µ (x) = (µ1 (x), µ2 (x)), for all x in G,

is a well-defined group homomorphism.

#### Solution Preview

...in G, we have

µ (a b) = ( µ1 (ab), µ2 (ab) ) = ( µ1 (a) µ1 (b), µ2 (a) ...