Examples of connections
The Parade Group
Here is an example of a group. The set of elements is the set containing the four parade commands: left face (L), right face (R), about face (A), and stand as you were (S). The operation is “followed by”, which we will designate as F.
Make a Cayley Table to show the results of each command followed by other commands.
Prove that the “Parade Group” really is a group. That is, show that the group axioms hold for the four commands and the operation  F “followed by”.