What is the First Isomorphism Theorem?

[proplaya201]

Homework Statement

can someone explain the 1st isomorphism theorem to me(in simple words) i really don't get it

Homework Equations

The Attempt at a Solution

 

[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!

 

[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.

 

[HallsofIvy]

If f: G-> H, then

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

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?

 

[proplaya201]

can you specify G/K is isomorphic to I.