With this core framework in place you can see how groups can be used to bring many different systems together in a way that you start to create sub-communities. Obviously, this section has many other features which could be added to it. From the top of my mind I can think of integration in terms of the following features that might make some interesting additions to the group section:
Messaging
You could create a "send to group" WYSIWYG section that sends messages to all the group members.
Additionally, you could integrate all the groups that a user is a member of into the messaging system so that the group name could be used as a contact name to blast messages directly from the mail section.
Friends
Group members can be integrated easily as friends.
Not only can you specify public, private, and friends' areas in your user profiles but also have a filter such as
members of groups I am part of
.
You obviously don't have to think only about how you can bring groups out to your other community...