Visual Group Theory, Lecture 4.6: Automorphisms

Visual Group Theory, Lecture 4.6: Automorphisms An automorphism is an isomorphism from a group to itself. The set of all automorphisms of G forms a group under composition, denoted Aut(G). After a few simple examples, we learn how Aut(Z_n) is isomorphic to U(n), which is the group consisting of set of integers relatively prime to n, where the operation is multiplication modulo n. Next, we look at automorphisms of both the dihedral group D_3 and the Klein 4-group V_4, and see how they can be thought of as "re-wirings" of the Cayley diagram. In both of these cases Aut(G) is a non-abelian group of order 6. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html