Symmetric Groups and Cycle Notation (A Surprising Symmetry) - Group Theory 002

An interesting take on the concept of symmetry leads us to discover one of the most important families of groups

0:00 - Intro
0:42 - A new kind of symmetry
2:18 - S4
3:10 - The symmetric groups
3:48 - The order of Sn
6:00 - Cyclic properties
11:10 - Decoding D4
12:37 - Converting to cycle notation
15:15 - Do all shuffles loop?
19:16 - Summing up
19:57 - Why the "symmetric" group?
20:22 - Embedding D4
22:00 - Next up