Automorphisms of the symplectic group over a local ring

Symplectic Automorphisms and the Picard Group of a K3 Surface

Let X be a K3 surface, and let G be a finite group acting on X by automorphisms. The action of G on X induces an action on the cohomology of X . We assume G acts symplectically: that is, G acts as the identity on H(X). In this case, the minimum resolution Y of the quotient X/G is itself a K3 surface. Nikulin classified the finite abelian groups which act symplectically on K3 surfaces by analyzi...

The Group of Automorphisms of a Distributively Generated Near Ring

S. D. Scott has shown that the group of automorphisms of the near ring generated by the automorphisms of a given group is isomorphic to the automorphism group of the given group if that group's automorphism is complete. Here that theorem is generalized by showing that the group of automorphisms of a near ring distributively generated by its units is a subgroup of the group of automorphisms of t...

On Marginal Automorphisms of a Group Fixing the Certain Subgroup

Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

The Dihedral Group D5 as a Group of Symplectic Automorphisms on K3 Surfaces

We prove that if a K3 surface X admits Z/5Z as a group of symplectic automorphisms, then it actually admits D5 as a group of symplectic automorphisms. The orthogonal complement to the D5-invariants in the second cohomology group of X is a rank 16 lattice, L. It is known that L does not depend on X: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. ...