ABSTRACT
So, with some sadness, we have arrived at the final chapter. Fear not, it is also one of the most exciting. In it, you will begin to see just how far one can get using just the four group axioms. For example, we’ll prove that if you have a finite group G, and you take any of its elements and raise it to the |G| th power, you always get the identity. We shall also see how groups can be applied in number theory — in particular, to help in finding the largest prime numbers known to mankind.
