Basics

This pages contains fundamental results of group theory.

Theorems

Theorem 1 (First Isomorphism Theorem)

Let \(G\) and \(H\) be two groups, and \(f\colon G\to H\) a homomorphism.
Let \(N\) be a normal subgroup of \(G\), and \(\varphi\colon G\to G/N\) the natural surjective homomorphism. If \(N\subseteq\ker f\), then there exists a unique homomorphism \(h\colon G/N\to H\) such that the following diagram commutes:

Proof. TODO