8 citations · 25 across the 10 of their papers we have counts for
10 papers
Stability, bounded generation and strong boundedness
Alexander Trost
We provide bounds linear in the rank for the generalized conjugacy diameters, introduced by Kedra, Libman and Martin, for the special linear and symplectic groups defined over the…
Elementary bounded generation for for global function fields and
Alexander Alois Trost
This paper shows that the group is boundedly elementary generated for and the ring of algebraic integers in a global function field. Contrary to previ…
The dichotomy property of -A short note
Alexander Alois Trost
A recent paper by Polterovich, Shalom and Shem-Tov has shown that non-discrete, conjugation invariant norms on arithmetic Chevalley groups of higher rank give rise to very restrict…
Bounded generation by root elements for Chevalley groups defined over rings of integers of function fields with an application in strong boundedness
Alexander A. Trost
Bounded generation by root elements is a property which has been widely studied for various types of linear algebraic groups defined over rings of integers in algebraic number fiel…
Strong boundedness of for rings of S-algebraic integers with infinitely many units
Alexander Alois Trost
A group is called strongly bounded, if the speed with which it is generated by finitely many conjugacy classes has a positive, lower bound only dependent on the number of the conju…
Bounded generation for congruence subgroups of
Alexander Alois Trost
This paper describes a bounded generation result concerning the minimal natural number such that for …
Explicit strong boundedness for higher rank symplectic groups
Alexander Trost
This paper gives an explicit argument to show strong boundedness for for a ring of S-algebraic integers or a semi-local ring. This gives a quantitative versi…
Strong boundedness of simply connected split Chevalley groups defined over rings
Alexander Alois Trost
This paper is concerned with the diameter of certain word norms on S-arithmetic split Chevalley groups. Such groups are well known to be boundedly generated by root elements. We pr…
Qualitative counting closed geodesics
Bastien Karlhofer, Jarek Kędra, Michał Marcinkowski +1
We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask wh…
Finite index subgroups in Chevalley groups are bounded: an addendum to "On bi-invariant word metrics"
Światosław R. Gal, Jarek Kędra, Alexander A. Trost
We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.