Access Denied - Security/Permission Setup Correctly

I have a DFS public shared folder and using inherited permissions/security from Parent. Then I want to add subfolders to the parent. Inside the subfolder I have added the individuals that need access to the folder (Full Access). They are able to get and open browse etc, but cannot create folders open/save documents? I have given them full access with their domain accounts. Please assist.
When saving file back to server it says READ ONLY. I checked the security\general and it has a read only checkmark I cannot remove it. When I remove and close the read only comes back on.