1. ## isomorphisms..direct product?

Say that [+] = external direct product of groups.
Given that,

Suppose that G is isomorphic to K and H is isomorphic to J. Prove that G[+]H is isomorphic to K[+]J

2. If $\phi:G\rightarrow K, \ \psi:H\rightarrow J$ are the isomorphisms, consider the map $\omega:G\oplus H\rightarrow K\oplus J$ defined by $\omega(g\oplus h)=\phi(g)\oplus\psi(h)$. Show this is an isomorphism.

3. Originally Posted by cowgirl123
Say that [+] = external direct product of groups.
Given that,

Suppose that G is isomorphic to K and H is isomorphic to J. Prove that G[+]H is isomorphic to K[+]J
See here