Orbits

We’re continuing our proofs of Sylow’s Theorems, and also continuing our efforts to count orbits, and determine the size of orbits created by the permutation groups…

In the previous entry, we gave a laborious proof that a group with an even number of elements has to have an element of order 2. We can do much better than that. We’ll show how by proving some famous theorems that were originally due to Sylow.