Classification of multiplicative Lie algebra structures on a finite group

Abstract

. Every multiplicative Lie algebra structure on a group G determines a group homomorphism from the exterior square G ∧ G to G . We give a precise character-ization of the group homomorphisms G ∧ 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.