For the third one, apply the first isomorphism theorem to the the projection homomorphism .
The map should be obviously surjective. For instance for any given .
Let and be groups and let [tex] G^\star [tex] be the subset of consisting of all with
Show the following:
2. is a normal subgroup of
I showed the first two just fine, but I'm having slight trouble with number 3. I had shown that it's a homomorphism, but the surjective part I'm stuck on. Could anyone guide me through this?