2020/04/28 by Segal, Dan, Tent, Katrin
#03C60 #20A15 #20G07 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)
paper · doi:10.48550/arxiv.2004.13407
We show that for Chevalley groups G(R) of rank at least 2 over a ring R the root subgroups are essentially (nearly always) the double centralizers of corresponding root elements. In very many cases 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.