Finite symplectic actions on the K3 lattice

In this paper, we study finite symplectic actions on K 3 surfaces X , that is, actions of finite groups G on X which act on H 2,0 ( X ) trivially. We show that the action on the K 3 lattice H 2 ( X , ℤ) induced by a symplectic action of G on X depends only on G up to isomorphism, except for five groups.