Hi @kimberly_hall1 ,
I could be wrong about this, however with I'm reasonably sure that by default students are not able to have view-only permissions on discussions assigned to other students. Generally, when a discussion, especially in a student group (if that's what you referencing) is created, all students in those groups are able to post on the discussion board, and when a student tries loading in a discussion not assigned to them or their group, it will take them to the course home-page, and will tell them they don't have access to the requested discussion.
I hope this helps answer your question!
All the best,
Noah