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}
}
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24 pages