3 papers
math.GR2025
Abstract isomorphisms of isotropic root graded groups over rings
Pavel Gvozdevsky
The celebrated Borel--Tits theorem provides a classification of abstract isomorphisms between (simple) isotropic groups over fields, showing that such isomorphisms arise from field…
math.GR2025
Regular bi-interpretability and finite axiomatizability of Chevalley groups
Elena Bunina, Pavel Gvozdevsky
In this paper we consider Chevalley groups over commutative rings with~, constructed by irreducible root systems of rank . We always suppose that for the systems $A_2, B_\el…
math.GR2024
Verbal width in arithmetic Chevalley groups
Pavel Gvozdevsky
We prove that the width of any word in a simply connected Chevalley group of rank at least 2 over the ring that is a localisation of the ring of integers in a number field is bound…