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Preprint Number 1771

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1771. Dan Segal and Katrin Tent
Defining R and G(R)

Submission date: 28 April 2020


We show that for Chevalley groups G(R) of rank at least 2 over a ring R the root subgroups are (nearly always) the double centralizer of a corresponding root element. If G(R) has finite elementary width, this implies that R and G(R) are bi-interpretable, yielding a new approach to bi-interpretability for algebraic groups over a wide range of rings and fields. For such groups it then follows that the group G(R) is finitely axiomatizable in the appropriate class of groups provided R is finitely axiomatizable in the corresponding class of rings.

Mathematics Subject Classification: 20A15, 20G07, 03C60

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Full text arXiv 2004.13407: pdf, ps.

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