Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory

The isomorphism theorem is a very useful theorem when it comes to proving novel relationships in group theory, as well as proving something is a normal subgroup. But not many people can understand it intuitively and remember it just as a kind of algebraic coincidence. This video is about the intuition behind the idea of homomorphism - functions preserving group structures, and the closely related isomorphism theorem.

There are second, third and even fourth isomorphism theorem (the fourth one is usually disputed), but all can be derived from the first one, using clever constructions of homomorphisms.

Apparently, when I was typing the description (after the video is edited), I knew that the name "homomorphism" is probably mistranslated from German. Originally, it was supposed to mean "similar", not "same".

This video series is about understanding the group theory intuitively, complementing how most people learn about it, because it is usually introduced as part of abstract algebra.

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