Hi Rose. This is a good question and I wondered about it myself. So, I did some experimentation and found something which can help you.
If you add a Wiki to your course, then under "Common module settings" you will see "Group mode." If you set "Group mode" to "Separate groups" then each student group will share their own Wiki. Note: You should set "Wiki mode" to "Collaborative wiki" since students will be collaborating with others who are in their group.
So, if you setup Group_1 which has Alice and Bob, then you setup Group_2 which has Charley and David, then Alice and Bob will share one Wiki. That is, when they click on the Wiki, they will edit it like it is an individual wiki. Neither Charley nor David will be able to see the work of Alice and Bob. Likewise, when Charley or David click on the Wiki, they will see only their own Wiki without any of the edits made by Alice or Bob. So, each group of students has a group wiki which is separate from other student groups.
With an "Individual" wiki, the teacher sees a drop down of student names so you can see each individual Wiki. However, with a Collaborative Wiki (with Group mode set to Separate groups) the teacher will now see the group names in that drop down.
My testing showed that it worked fine. I am going to actually use it for my class this coming semester.