Amalgams of rational unipotent groups and residual nilpotence

2024/02/22 by Caprace, Pierre-Emmanuel, Marquis, Timothée
#20E06 #20E26 #20F14 #20F65 #20F67 #20G44 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.14507

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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