Abstract Algebra

The Intuition Behind the Isomorphism Theorems

A Visual Explanation of the Three Isomorphism Theorems

At first glance, the isomorphism theorems may seem confusing and unintuitive. The goal of this article is to hopefully give you additional insight into what the isomorphism theorems are trying to say. To make things more simple, we will only look at the theorems in the context of groups. Consider the three isomorphism theorems stated for groups. Let \(G\) and \(H\) be groups and let \(\varphi: G\to H\) be a homomorphism.