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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…
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…
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.