Abstract Algebra. Isomorphisms 1: Introduction

Title: Isomorphisms 1: Introduction

Abstract: We give an introduction to isomorphisms. Roughly speaking, two groups are isomorphic if they have the same size and the same structure. In this introductory video, we do not give the rigorous definition of an isomorphism, but we instead consider two finite groups to be isomorphic if we can draw their multiplication tables in such a way so that all of the elements line up.

It turns out that there are two "different types" of groups of size four: those that are isomorphic to Z_4 (the cyclic group of order four) and those that are isomorphic to Z_2 x Z_2 (the Klein four-group).