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

Abstract

We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) that are generated by the affine subgroup and a nonaffine 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 product of the affine group and a finite group over their intersection.

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Recommended citation: E. Edo & __D. Lewis__, The affine automorphism group of $\mathbb{A}^3$ is not a maximal subgroup of the tame automorphism group, _Michigan Mathematics Journal_, 64(3) (2015), 555-568.