# Homework Help: Abstract Algebra; Group Theory Question

1. Mar 11, 2015

### tropian1

• Member warned about posting without the template and with no effort
Let N be a normal subgroup of a group G and let f:G→H be a homomorphism of groups such that the restriction of f to N is an isomorphism N≅H. Prove that G≅N×K, where K is the kernel of f.

I'm having trouble defining a function to prove this. Could anyone give me a start on this?

2. Mar 11, 2015

### micromass

Start by proving the following:
1) $N$ and $K$ are normal
2) $NK = G$
3) $N\cap K = \{e\}$