Finite-order automorphisms of a certain torus

Finite-order Automorphisms of a Certain Torus

A classical result of Higman [H], [S, Exer. 6.3], asserts that the roots of unity in the group ring Z[Γ] of a finite commutative group Γ are the elements ±γ for γ ∈ Γ. One application of this result is the determination of the group of finite-order automorphisms of a torus T = ResS′/S(Gm) for a finite étale Galois covering f : S′ → S with S and S′ connected schemes and abelian Galois group Γ = ...

Stable Ergodicity of Certain Linear Automorphisms of the Torus

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) ...

Automorphisms of Finite Order on Rational Surfaces

Ž . We classify minimal pairs X, G for smooth rational projective surface X and finite group G of automorphisms on X. We also determine the fixed locus X G and the quotient surface Y X G as well as the fundamental group of the smooth part of Y. The realization of each pair is included. Mori’s extremal ray theory and recent results of Alexeev and also Ambro on the existence of good anti-canonica...

Bounding the Order of Automorphisms of Certain Curves

We study upper bounds on the order of automorphisms of non-singular curves X satisfying at least one of the following hypothesis: 1) X is an m-sheeted covering of exactly one non-singular curve of genus γ, where m is prime; 2) the center of the group of automorphisms of X is non-trivial. Notation. Throughout this paper, by a curve we mean a non-singular, irreducible and projective algebraic cur...