Laila Mohamed
New member
- Joined
- Oct 11, 2022
- Messages
- 1
Hi, I have a homework but I can't solve it. Can someone help me ?
Let ϕ : G → H be a homomorphism of groups.
Show that if ϕ is an isomorphism of groups, then its inverseϕ−1:H→G,ϕ(g)→ϕ−1(ϕ(g))=g, is an isomorphism of groups.
I know that ker(ϕ) = e ⇐⇒ injective, but I don't know how to proceed and I completely don't know how to prove that this is surjective too.
Let ϕ : G → H be a homomorphism of groups.
Show that if ϕ is an isomorphism of groups, then its inverseϕ−1:H→G,ϕ(g)→ϕ−1(ϕ(g))=g, is an isomorphism of groups.
I know that ker(ϕ) = e ⇐⇒ injective, but I don't know how to proceed and I completely don't know how to prove that this is surjective too.