"The definition of groups is... everyone inside the group knows who else is in the group"

This is a slightly narrow definition, the visibility of a group should be an attribute.

Dan Gillmor cites a good use-case:

"I'm considering a circle called "insufferable" for people I find personally annoying but whose work I feel obliged to keep track of, in any case."

http://www.guardian.co.uk/commentisfree/cifamerica/2011/jun/...