Polynomial mappings of groups

@article{Leibman2002PolynomialMO,
  title={Polynomial mappings of groups},
  author={A. Leibman},
  journal={Israel Journal of Mathematics},
  year={2002},
  volume={129},
  pages={29-60}
}
  • A. Leibman
  • Published 2002
  • Mathematics
  • Israel Journal of Mathematics
A mapping ϕ of a groupG to a groupF is said to be polynomial if it trivializes after several consecutive applications of operatorsDh,h ∈G, defined byDhϕ(g)=ϕ(g)−1ϕ(gh). We study polynomial mappings of groups, mainly to nilpotent groups. In particular, we prove that polynomial mappings to a nilpotent group form a group with respect to the elementwise multiplication, and that any polynomial mappingG→F to a nilpotent groupF splits into a homomorphismG→G’ to a nilpotent groupG’ and a polynomial… Expand
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