When creating a User Group I picked the option where the Group was visible to all users but required "an invitation" to join. That's not how the module behaves, however. It does not require an invitation to join...it simply requires approval before somebody can join.
The way it's worded now it seems like a person would not be able to request joining until they got an invitation. Makes a potential user group creator think, "I'm going to have to send invitations out to people to join this group" when in truth users can request to join on their own.