This is the "registered" group. Their base permissions do not allow them to start new threads or reply to threads. But they can edit their own posts.
For the "registration" forum, I have a permission override for this group, allowing them to start new threads and reply to threads. They are inheriting the "edit own posts" permission.
The registered group is able to start new threads and reply to threads in the registration forum. But they are unable to edit their own posts.