I am familiar with the first isomorphism theorem, but looking on wikipedia I see this image which I do not understand.
http://en.wikipedia.org/wiki/File:First-isomorphism-theorem.svg
A few specific questions about it:
- What do the arrows coming from/ leading to a $0$ mean? Are they different from the other arrows? Also, since I clearly don't understand the diagram, I might as well ask what the other arrows mean too.
- How am I supposed to read the diagram? Naturally I want to start at the $0$ in the bottom left and go from $\ker f$ to $G/\ker f$.
- It seems like the whole statement of the theorem is contained in the one block $G/\ker f \simeq \operatorname{im} f$ so what is the point of the rest of the diagram?