11 citations · 23 across the 20 of their papers we have counts for
7 papers · 1 filter
Torsion in asymptotic cones of free groups
Jarek Kędra, Assaf Libman, Zipei Nie
We prove that the asymptotic cone of any non-abelian free group equipped with the bi-invariant word metric has elements of order 2.
Are free groups of different ranks bi-invariantly quasi-isometric?
Jarek Kędra, Assaf Libman
We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics is a quasi-isometry if and only if it is an isomorphism.
Directional asymptotic cones of groups equipped with bi-invariant metrics
Jarek Kędra, Assaf Libman
Given a bi-invariant metric on a group, we construct a version of an asymptotic cone without using ultrafilters. The new construction, called the directional asymptotic cone, is a…
Uniform boundedness for algebraic groups and Lie groups
Jarek Kędra, Assaf Libman, Ben Martin
Let be a semisimple linear algebraic group over a field and let be the subgroup generated by the subgroups , where ranges over all the minimal -p…
Punctured groups for exotic fusion systems
Ellen Henke, Assaf Libman, Justin Lynd
The transporter systems of Oliver and Ventura and the localities of Chermak are classes of algebraic structures that model the -local structures of finite groups. Other than the…
Strong and uniform boundedness of groups
Jarek Kędra, Assaf Libman, Ben Martin
A group G is called bounded if every conjugation-invariant norm on G has finite diameter. We introduce various strengthenings of this property and investigate them in several class…