CLASSIFICATION OF MULTIPLICATIVE LIE ALGEBRA STRUCTURES ON A FINITE GROUP

Every multiplicative Lie algebra structure on a group G determines a group homomorphism from the exterior square G perpendicular to G to G. We give a precise characterization of the group homomorphisms G perpendicular to G -> G which determine a multiplicative Lie algebra structure on G. For certain finite groups, we determine the number of possible images (up to isomorphism) of such structure-defining maps.