The Hidden option for Groups does not work - it simply hides all the activities with a Group restriction and as a result students see an empty page (activities are invisible). To ensure that students see the activities, you need to edit Group settings to at least "Own membership only" but in that case students can view their own membership, which is not desired in my case. 

1. Create two test accounts for "Student A" and "Student B". These should be Student accounts.
2. Create two groups, Group A and Group B.
3. In the settings of each Group, select the option "Hidden" - the last option.
4. In the course create two activities, for example Text and Media area, called Activity for group A and Activity for group B.
5. In the settings of Activity for group A add a restriction "Student must belong to Group A"
6. In the settings of Activity for group B add a restriction "Student must belong to Group B"
7. Assign Student A to Group A and Student B to Group B.
8. In a private window or different browser, log in as Student A and display the course. Do the same for Student B.
9. The expected result is that each student can see only 1 activity, according to the restriction but instead the activities created in step 4 are not visible for any student in any group - they simply disappear.
10. To verify, remove each test student from each group.
11. Change the settings of each group to "Own membership only"
12. Reassign both students to their respective groups (repeat step 7). 
13. Refresh the course while logged in as each student.
14. The activities are now displayed as intended - each student can see only one activity.