Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms

Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplication tables to understand why this condition means that homomorphism are "structure preserving" maps. Along the way, we see some new groups, such as the roots of unity, and groups of matrices, that end up being isomorphic to groups that we familiar with. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html