Thank you Peter for this work around. I am using Moodle 2.2 and there is still an issue with the visible group settings. As a teacher I could not see the different groups and was unable to assess the work of my students when working in groups using the wiki. As I consider the collaborative work using the wiki on of the most important part of my course I was seriously considering going back to 1.9. Your work around saved me.
Here are some additional hints to make it a bit easier for the students and the teacher when using the visible group mode.
Create a horizontal line menu in the Wiki description using:
Wiki administation -> Edit settings
I linked each team to their wiki as described by Peter. To make it easier for me, I forced each team to have the same first page name ( in my case http://......../mod/wiki/view.php?wid=7&title=Company&group=2) and all you have to do is change the group number for each group. (I am not sure but different names for the first page with each group might be part of the problem). I normally create an empty first page for each group and once created the editing members of a group can't change the name of that first page.
To save vertical space, I only put the one line menu in the Wiki description - the Wiki description shows at the top on each created parent and child wiki pages. Students see only the menu bar at the top of each wiki page. You have to instruct the students not to use the wiki's pull-down group selection menu.
I give the instructions for the activity on a different page I only can edit. All you have to do is create a group with only the teacher and non-editing teacher as a member. Because the group mode is "visible" all the students can see the information (in my case I called the link "Useful Information")
I had a quick look to see if I could change the code of the wiki's pull-down group selection menu and change it with Peter's parameters. I hope somebody with more time and Moodle code knowledge can fix this problem.
I have used many different LMS platforms but Moodle is the best. Thank you to all of you who have contributed to this excellent Open Source software. I could not teach without it!