# 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}
}
• Published 3 October 2014
• Mathematics
• arXiv: Algebraic Geometry
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…

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