English

Amalgams of rational unipotent groups and residual nilpotence

Group Theory 2026-04-13 v1

Abstract

We provide sufficient conditions for a free amalgamated product of torsionfree nilpotent groups to be residually nilpotent. We also characterise the residual nilpotence of certain higher-dimensional amalgams of unipotent groups over the rationals (known as KMS groups) in terms of their defining Cartan matrix. As an application, we give a normal form for the elements of a minimal Kac-Moody group over the rationals.

Keywords

Cite

@article{arxiv.2402.14507,
  title  = {Amalgams of rational unipotent groups and residual nilpotence},
  author = {Pierre-Emmanuel Caprace and Timothée Marquis},
  journal= {arXiv preprint arXiv:2402.14507},
  year   = {2026}
}

Comments

24 pages