R-Automorphisms of finite order in R〚X〛

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...

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 = ...

Automorphisms of Finite Order on Rational Surfaces ( with an Appendix

Finite Groups with Fixed-point-free Automorphisms of Prime Order.

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Automorphisms of Finite Fields

Let F be a finite field, and 4: F* + E a surjective group homomorphism from the multiplicative group F* of F to a non-trivial abelian group E. A theorem of McConnel (Acta Arith. 8 (1963) 127-151) describes the permutations e of F with the property that d(ux uy) = d(x y) for all X, j’ E F, .Y #J. We give a short proof of this theorem, based on an argument of Bruen and Levinger (Canad. J. Math. 2...