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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 thisconjectural Leibniz homology should satisfy, namely the existence of acoZinbiel coalgebra structure on rack homology and the existence of a nontrivial natural cocommutative coalgebra morphism from the rack homology of agroup to its Eilenberg-MacLane homology. The end of the paper treats theparticular cases of the linear group and of abelian groups. We prove theexistence of a connected coZinbiel-associative bialgebra structure on theirrack homology.

Rack homology and conjectural Leibniz homology