The Schur Multiplier of Some Finite Multiplicative Lie Algebras

Key Points

• The aim is to classify multiplicative Lie algebra structures on specific groups and determine their Schur multipliers.
• Classified multiplicative Lie algebra structures on symmetric and alternating groups.
• Calculated the Schur multiplier and Lie exterior square for finite multiplicative Lie algebras.
• Analyzed non abelian simple groups with trivial Schur multipliers.
• Identified all multiplicative Lie algebra structures on symmetric and alternating groups.
• Found that the Schur multiplier for non abelian simple groups is trivial if their Schur multiplier is trivial.
• Showed that the Lie exterior square of non abelian groups is isomorphic to the group itself with an improper structure.