102 citations · 204 across the 29 of their papers we have counts for
34 papers
Bounded elementary generation of SL_2: nearly the end
B. E. Kunyavskii, D. W. Morris, A. S. Rapinchuk
Let be the ring of -integers of a global field of any characteristic, where is a finite set of valuations of (and contains all of the archimedean…
The congruence subgroup property for -arithmetic subgroups of simple algebraic groups when has positive Dirichlet density
Andrei S. Rapinchuk
Let be an absolutely almost simple simply connected algebraic group defined over a number field , and let be the minimal Galois extension over which becomes an inn…
Are Widely Known Findings Easier to Retract?
Shahan Ali Memon, Jevin D. West, Cailin O'Connor
Failures of retraction are common in science. Why do they occur? And what determines whether a retraction is successful? We use data from citation records and Altmetrics to test pr…
Purely exponential parametrizations and their group-theoretic applications
Pietro Corvaja, Julian Demeio, Andrei Rapinchuk +2
This paper is mainly motivated by the analysis of the so-called Bounded Generation property (BG) of linear groups (in characteristic ), which is known to admit far-reaching grou…
The finiteness of the Tate-Shafarevich group over function fields for algebraic tori defined over the base field
Andrei S. Rapinchuk, Igor A. Rapinchuk
Let be a field and be a set of rank one valuations of . The corresponding Tate-Shafarevich group of a -torus is $Sha(T , V) = \ker\left(H^1(K , T) \to \prod_{v \i…
Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings
Peter Abramenko, Andrei S. Rapinchuk, Igor A. Rapinchuk
We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive…