I am having some troubles to understand what the difference is between discrete and finite groups. I know they are defined differently, I can't quite understand the difference. I am guessing every finite group but the viceversa is not true. Could someone make this clear and give an example?
Thanks, Eduardo
These are completely different objects.
A finite group is just that, a group with finitely many elements.
A discrete group is a topological group, where the topology is discrete.
An example of a finite, but not discrete group is ANY finite group with no topology on it, or not the discrete one.
An example of discrete, but not finite group is ANY infinite group with the discrete topology.