How can you rename pages in folders?

I have folders set up for each group of students working on a project. I don't want them to see other group's work, so I set up folder security. I also don't want them to edit information on the rest of the wiki (resources I created, syllabus, etc.) or to add pages outside of their folders, so I made them all readers for their main security. No matter what level of security I set up for them in their particular folders, they are unable to rename pages within their folders. The message they receive is that they have reader level security. How do I set it up so that students can add, delete and rename pages within their folders only while still having read access to the materials outside of the secure folders?