Continuing the discussion from What does selecting "Primary Group" for a user do?:
From what I can tell, when members are in multiple groups one of the groups can be named as their primary group, but this can only be set by an administrator via the admin user screen.
Would it be reasonable to let the user decide for herself – i.e., add a this setting to the user's preference page? Or possibly as a feature on the new & improved Groups page (when viewing a non-primary group for whom your a member, you see a "make this my primary group" button)?