# Homework Help: First isomorphism theorem

1. Nov 4, 2008

### proplaya201

1. The problem statement, all variables and given/known data

can someone explain the 1st isomorphism theorem to me(in simple words) i really dont get it

2. Relevant equations

3. The attempt at a solution

2. Nov 4, 2008

### sutupidmath

Why don't you write down the 1st isomorphism theorem, so people here will actually know what are you talking about. Not everybody might have learned that theorem adressed with the same name as you!

3. Nov 4, 2008

### proplaya201

If G and H are groups and f is a homomorphism from G to H, then the kernel K of f is a normal subgroup of G, the image of f is a subgroup of H, and the quotient group G /K is isomorphic to the image of f.

4. Nov 4, 2008

### HallsofIvy

If f: G-> H, then

The kernel, K, of f is a subgroup of G - {x in G such that f(G)= eH}

The Image, I, of f is a subgroup of H- {y in H such that y= f(x) for some x in G}

1) K is a normal subgroup of G.

2) G/K is isomorphic to I.

Do you understand what "homomorphism" and "isomorphism" mean? Do you understand what a "normal subgroup" is and what "G/K" is?

5. Nov 4, 2008

### proplaya201

can you specify G/K is isomorphic to I.