24 citations · 43 across the 17 of their papers we have counts for
19 papers
Bounded generation of Steinberg groups over Dedekind rings of arithmetic type
Boris Kunyavskii, Andrei Lavrenov, Eugene Plotkin +1
The main result of the present paper is bounded elementary generation of the Steinberg groups for simply laced root systems of rank and arbitrary Ded…
Uniform bounded elementary generation of Chevalley groups
Boris Kunyavskii, Eugene Plotkin, Nikolai Vavilov
In this paper we establish a definitive result which almost completely closes the problem of bounded elementary generation for Chevalley groups of rank over arbitrary Dedek…
The Diophantine problem in Chevalley groups
Elena Bunina, Alexey Miasnikov, Eugene Plotkin
In this paper we study the Diophantine problem in Chevalley groups , where is an indecomposable root system of rank , is an arbitrary commutative ring with $…
Bounded generation and commutator width of Chevalley groups: function case
Boris Kunyavskii, Eugene Plotkin, Nikolai Vavilov
We prove that Chevalley groups over polynomial rings and over Laurent polynomial rings, where is a finite field, are boundedl…
Elementary equivalence of Kac-Moody groups
Jun Morita, Eugene Plotkin
The paper is devoted to model-theoretic properties of Kac-Moody groups with the focus on elementary equivalence of Kac-Moody groups. We show that elementary equivalence of (untwist…
Group-like small cancellation theory for rings
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free gr…