I would like to suggest new group type: Invite Only Group (by admins only)
So only group's admin can invite new members.
Or may be you can improve Invite Only Group by allowing admins moderate new members before they join group?
There is no innovation here -- such group type we can see in VK.com social network and others.
It's important if admins :
1) have top-secret group
2) or have paid group
and dooesn't want to let current members invite new members without admin's approve (or for free).
Thanks.