  We study the fair division of items to agents supposing that agents can form
groups. We thus give natural generalizations of popular concepts such as
envy-freeness and Pareto efficiency to groups of fixed sizes. Group
envy-freeness requires that no group envies another group. Group Pareto
efficiency requires that no group can be made better off without another group
be made worse off. We study these new group properties from an axiomatic
viewpoint. We thus propose new fairness taxonomies that generalize existing
taxonomies. We further study near versions of these group properties as
allocations for some of them may not exist. We finally give three prices of
group fairness between group properties for three common social welfares (i.e.
utilitarian, egalitarian, and Nash).
