Hi Bruno,
This is actually very easy to implement.
At the moment you have created groups for each of the study groups, and presumably placed users within these groups.
When you create your forum, just set the Group Mode (in Common Module Settings) to "Separate Groups".
I would recommend that you also create a Grouping of your various groups, which you can then select at the same time as the group mode.
Groupings are designed to bring together a collection of related groups to be used in an activity.
For example, you might have a piece of group work where your students are expected to work together as a team and submit a brief of their work. They may want to discuss that work in a forum, and then several weeks later they submit the final product in an assignment . To do so, you can create 5 groups for your students for this activity. You would create a single grouping containing all five of these groups. You can then select this Grouping (of groups) when setting up the assignments and forums for your group work. Later on, you place students in a different set of groups for a new piece of group work. You would create your new groups, and new grouping for this. If you had not created and used the groupings, both activities would see every group in the course, which can quickly become confusing to students.
Andrew