Hi Thomas,
Edocman manages permissions in the system using Joomla ACL (Access Control List).
You can read more details about how this works here:
docs.joomdonation.com/edocman/getting-started/edocman_acl
Basically, if a user belongs to a group that does not have permission to upload documents, they will not be able to do so, and the Upload button won't show anymore.
Let me know if you have any further questions!
Best regards,
Dam