- #1

- 19

- 2

- Homework Statement:
- Prove G X H is a group.

- Relevant Equations:
- N/A

So I that I need to prove the axioms: associativity, existence of the identity element, and existence of the right inverse.

For associativity I know that the binary operations of G and H have to already be associative, and the elements of G X H are made up of these binary operations, so therefore it is associative?

For identity element let G have identity element e, and H have identity element f, can the identity element of G X H have the set (e,f), so that if (x,y) are included in G X H then (e,f) * (x,y) = (x,y) = (x,y) * (e,f)?

For the right inverse I am stuck, I don't know how to find it without knowing what the binary operations actually do.

For associativity I know that the binary operations of G and H have to already be associative, and the elements of G X H are made up of these binary operations, so therefore it is associative?

For identity element let G have identity element e, and H have identity element f, can the identity element of G X H have the set (e,f), so that if (x,y) are included in G X H then (e,f) * (x,y) = (x,y) = (x,y) * (e,f)?

For the right inverse I am stuck, I don't know how to find it without knowing what the binary operations actually do.