Finite groups of automorphisms of K3 surfaces and the Mathieu group (Q917639)

The article under review classifies the finite groups which have symplectic actions on a K3 surface S, i.e. which fixes a nowhere zero holomorphic 2-form w on S. It is shown that these finite groups coincide with the finite groups which have certain types of embeddings into the Mathieu group \(M_{24}\). This completes the work of Nikulin, who classified the symplectic actions of finite abelian groups.