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Amalgams of rational unipotent groups and residual nilpotence
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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.
European Mathematical Society - EMS - Publishing House GmbH
Title: Amalgams of rational unipotent groups and residual nilpotence
Description:
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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