There Is No Tame Automorphism of C 3 with Multidegree (3, 4, 5)

TAME AUTOMORPHISMS OF C 3 WITH MULTIDEGREE OF THE FORM (3, d2, d3)

In this note we prove that the sequence (3, d2, d3), where d3 ≥ d2 ≥ 3, is the multidegee of some tame automorphism of C if and only if 3|d2 or d3 ∈ 3N + d2N.

The Tame and the Wild Automorphisms of Polynomial Rings in Three Variables

Let C = F [x1, x2, . . . , xn] be the polynomial ring in the variables x1, x2, . . . , xn over a field F , and let AutC be the group of automorphisms of C as an algebra over F . An automorphism τ ∈ AutC is called elementary if it has a form τ : (x1, . . . , xi−1, xi, xi+1, . . . , xn) 7→ (x1, . . . , xi−1, αxi + f, xi+1, . . . , xn), where 0 6= α ∈ F, f ∈ F [x1, . . . , xi−1, xi+1, . . . , xn]....

Defining relations of the tame automorphism group of polynomial algebras in three variables

We describe a set of defining relations of the tame automorphism group T A 3 (F) of the polynomial algebra F [x 1 , x 2 , x 3 ] in variables x 1 , x 2 , x 3 over an arbitrary field F of characteristic 0.

Corrigendum Parallelisms of P G(3, 4) with Automorphisms of Order 5

A spread is a set of lines of PG(d, q), which partition the point set. A parallelism is a partition of the set of lines by spreads. Some constructions of constant dimension codes that contain lifted MRD codes are based on parallelisms of projective spaces. A parallelism is transitive if it has an automorphism group which is transitive on the spreads. A parallelism is point-transitive if it has ...

Decidability and Tameness in the Theory of Finite Semigroups