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

@article{Edo2014TheAA, title={The affine automorphism group of A^3 is not a maximal subgroup of the tame automorphism group}, author={Eric Edo and Drew Lewis}, journal={arXiv: Algebraic Geometry}, year={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 automorphism. One important corollary is the titular result that settles negatively the open question (in characteristic zero) of whether the affine subgroup is a maximal subgroup of the tame automorphism group. We also prove that all groups of this family have the structure of an amalgamated free…

## 7 Citations

### NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM

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We study criteria for deciding when the normal subgroup generated by a single special polynomial automorphism of 𝔸n is as large as possible, namely, equal to the normal closure of the special linear…

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### A non-tame and non-co-tame automorphism of the polynomial ring

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- 2020

An automorphism $F$ of the polynomial ring in $n$ variables over a field of characteristic zero is said to be {\it co-tame} if the subgroup of the automorphism group of the polynomial ring generated…

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- 2020

In this paper, we discuss subgroups of the automorphism group of the polynomial ring in n variables over a field of characteristic zero. An automorphism F is said to be {\it co-tame} if the subgroup…

### STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS

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We say that a polynomial automorphism ϕ in n variables is stably co-tame if the tame subgroup in n variables is contained in the subgroup generated by ϕ and affine automorphisms in n+1 variables. In…

### STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS

- MathematicsTransformation Groups
- 2017

We say that a polynomial automorphism ϕ in n variables is stably co-tame if the tame subgroup in n variables is contained in the subgroup generated by ϕ and affine automorphisms in n+1 variables. In…

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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.

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