The Schur Multiplier of Some Finite Multiplicative Lie Algebras

We classify all the multiplicative Lie algebra structures on symmetric groups and alternating groups. We also determine the Schur multiplier and the Lie exterior square of some finite multiplicative Lie algebras. For a non abelian simple group K with trivial Schur multiplier, we see that the Schur multiplier of multiplicative Lie algebra K is trivial and the Lie exterior square of K is isomorphic to K with improper multiplicative Lie algebra structure.