2. Homomorphisms and Isomorphisms

Question 1

What is the definition of a normal subgroup?

Answer 1

Definition 2.3: A subgroup N ≤ G is called normal if n∈N,g∈G =⇒ gng−1 ∈N.
This is denoted by N ⊴ G.

Question 2

Let φ : G → H be a group homo- morphism and x ∈ G. The following hold:

Answer 2

1)φ(eG) = eH;
2)φ(x−1) = φ(x)−1;
3)φ(xn) = φ(x)n for all n ∈ Z.