  This article presents results being consistent with conjectures of J.-L.
Loday about the existence and properties of a Leibniz homology for groups.
Introducing L-sets we prove that (pointed) rack homology has properties this
conjectural Leibniz homology should satisfy, namely the existence of a
coZinbiel coalgebra structure on rack homology and the existence of a non
trivial natural cocommutative coalgebra morphism from the rack homology of a
group to its Eilenberg-MacLane homology. The end of the paper treats the
particular cases of the linear group and of abelian groups. We prove the
existence of a connected coZinbiel-associative bialgebra structure on their
rack homology.
