5 citations · 21 across the 13 of their papers we have counts for
13 papers
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…
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…
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…
On countable isotypic structures
Pavel Gvozdevsky
We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; th…
Bounded reduction for Chevalley groups of types and
Pavel Gvozdevsky
We prove that an element from the Chevalley group of type or over a polynomial ring with coefficients in a small-dimensional ring can be reduced to an element of certai…
Width of SL(n,O_S,I)
Pavel Gvozdevsky
We give an estimate for the width of the congruence subgroup in Tits--Vaserstein generators, where is a localisation of the ring of integers in a numbe…
Twisted forms of commutative monoid structures on affine spaces
Andrei V. Semenov, Pavel Gvozdevsky
In this paper, we study affine commutative algebraic monoid structures on affine spaces over an arbitrary field of characteristic zero. We obtain full classification of such struct…
Overgroups of subsystem subgroups in exceptional groups: nonideal levels
Pavel Gvozdevsky
In the present paper, we practicaly complete the solution of the problem on the description of overgroups of the subsystem subgroup in the Chevalley group over th…
Overgroups of subsystem subgroups in exceptional groups: inside a sandwich
Pavel Gvozdevsky
The current paper is an addition to the previous paper by author, where the overgroup lattice of the elementary subsystem subgroup of the Chevalley group for a la…
Bounded reduction of orthogonal matrices over polynomial rings
Pavel Gvozdevsky
We prove that a matrix from the split orthogonal group over a polynomial ring with coefficients in a small-dimensional ring can be reduced to a smaller matrix by a bounded number o…
Improved -stability for the embedding into
Pavel Gvozdevsky
This paper is dedicated to the surjective stability of the -functor for Chevalley groups for the embedding into . This case was already studed by Plotkin. In the pr…
Overgroups of subsystem subgroups in exceptional groups: 2A1-proof
Pavel Gvozdevsky
In the present paper we prove a weak form of sandwich classification for the overgroups of the subsystem subgroup of the Chevalley group where is a simply lac…
Overgroups of Levi subgroups I. The case of abelian unipotent radical
Pavel Gvozdevsky
In the present paper we prove sandwich classification for the overgroups of the subsystem subgroup of the Chevalley group for the three types of pair (the…