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arXiv · 2402.14507

Amalgams of rational unipotent groups and residual nilpotence

Pierre-Emmanuel Caprace·Timothée Marquis
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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.

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Pierre-Emmanuel Caprace, Timothée Marquis. 2024-02-22. Amalgams of rational unipotent groups and residual nilpotence. https://doi.org/10.4171/jca%2F126

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