BuddyPress.org

There is a plugin by Burt called Community Groups, and this will help you do what hempsworth is describing (and what you are requesting) quite easily. Do a search for some of the topics I’ve posted in recently, and you’ll find it somewhere in there.

Otherwise you could just manually add each member of the group as a user/editor of the blog, which will provide you the same functionality but obviously be more tedious as members join and leave the group.