Since there are pages for blogs and polls on our profiles, why not one for our groups?
However, maybe create a setting where we can toggle which groups we would like to be made public, since I'm sure I'm not the only one with groups that don't need to be seen.
I also think it would be kind of cool to request invites that way too; maybe some little button in the list to send a request to the group owners.
I also think we should have the option to maybe type out a little discription (optionally, of course) for each group so members would know what they're getting into beforehand.