# NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM

@article{Lewis2017NORMALSG, title={NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM}, author={Drew Lewis}, journal={Transformation Groups}, year={2017}, volume={25}, pages={177-189} }

We study criteria for deciding when the normal subgroup generated by a single special polynomial automorphism of 𝔸 n is as large as possible, namely, equal to the normal closure of the special linear group in the special automorphism group. In particular, we investigate m-triangular automorphisms , i.e., those that can be expressed as a product of affine automorphisms and m triangular automorphisms. Over a field of characteristic zero, we show that every nontrivial 4-triangular special…

## References

SHOWING 1-10 OF 19 REFERENCES

### The affine automorphism group of A^3 is not a maximal subgroup of the tame automorphism group

- Mathematics
- 2014

We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tame…

### Normal subgroup generated by a plane polynomial automorphism

- Mathematics
- 2010

We study the normal subgroup 〈f〉N generated by an element f ≠ id in the group G of complex plane polynomial automorphisms having Jacobian determinant 1. On the one hand, if f has length at most 8…

### Polynomial automorphisms over finite fields: Mimicking non-tame and tame maps by the Derksen group.

- Mathematics
- 2009

If F is a polynomial automorphism over a finite field Fq in dimen- sion n, then it induces a bijectionqr(F) of (Fqr) n for every r 2 N � . We say that F can be 'mimicked' by elements of a certain…

### Acylindrical hyperbolicity of the three-dimensional tame automorphism group

- Mathematics
- 2016

We prove that the group STame($k^3$) of special tame automorphisms of the affine 3-space is not simple, over any base field of characteristic zero. Our proof is based on the study of the geometry of…

### GENERALISATIONS OF THE TAME AUTOMORPHISMS OVER A DOMAIN OF POSITIVE CHARACTERISTIC

- Mathematics
- 2013

In this paper, we introduce two generalizations of the tame subgroup of the automorphism group of a polynomial ring over a domain of positive characteristic. We study detailed structures of these new…

### The tame and the wild automorphisms of polynomial rings in three variables

- Mathematics
- 2003

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 ∈…

### Normal subgroups in the Cremona group

- Mathematics
- 2010

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane $$ \mathbb{P}_{\mathbf{k}}^2 $$ is not a simple group. The strategy…

### Co-tame polynomial automorphisms

- MathematicsInt. J. Algebra Comput.
- 2019

It is shown that the statement "Every $m$-triangular automorphism is either affine or co-tame" is true if and only if $m \leq 3$; this improves upon positive results of Bodnarchuk and negative results of the authors.

### Acylindrical hyperbolicity of groups acting on trees

- Mathematics
- 2013

We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, one-relator groups,…

### Algebraic theory of locally nilpotent derivations

- Mathematics
- 2006

First Principles.- Further Properties of Locally Nilpotent Derivations.- Polynomial Rings.- Dimension Two.- Dimension Three.- Linear Actions of Unipotent Groups.- Non-Finitely Generated Kernels.-…