Facebook groups are one area of the site where you don't need to be friends with another user in order to interact with him. Whether or not you are friends within someone, the only course of action you can take as a group administrator is to suggest the group or approve requests to join; it isn't possible to add anyone, friend or not, to a group without him first expressing interest in the group through a request.
Sign in to Facebook. Click your profile name or picture in the upper left corner of the site, then select "Groups."
Select "Requests to Join Group" from the menu on the right side of the group. Click the "Approve" button next to each member that you want to approve and add to the group.
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Interact with new, non-friend group menus. Add a member to your list of friends if you want to see her full Facebook profile, communicate via chat and comment on or "like" her posts.