2 citations · 4 across the 10 of their papers we have counts for
8 papers · 1 filter
Small Kazhdan constants for small generating sets of linear groups
Tsachik Gelander, Alex Lubotzky, Jvbin Yao
Let G be a linear group with Kazhdan property (T) generated by d elements. We show that there are generating sets of size d+2 with arbitrarily small Kazhdan constants. We also prov…
Non Uniform Kazhdan Constant for Linear Groups
Alexander Lubotzky, Jvbin Yao
A group generated by a finite set has Property if the associated Kazhdan constant is positive. If so, the same holds for every finite generating set . The…
Subgroups with all finite lifts isomorphic are conjugate
Ido Karshon, Alexander Lubotzky, D. B. McReynolds +2
We show that for non-conjugate subgroups and of a finite group there exists an extension of (by a finite group) in which the pre-images of and are n…
On -approximation of groups
Benjamin Bachner, Alon Dogon, Alexander Lubotzky
A longstanding open problem in the intersection of group theory and operator algebras is whether all groups are MF, that is, approximated by asymptotic representations with respect…
The Aldous--Lyons Conjecture I: Subgroup Tests
Lewis Bowen, Michael Chapman, Alexander Lubotzky +1
This paper, and its companion [BCV24], are devoted to a negative resolution of the Aldous--Lyons Conjecture [AL07, Ald07]. This conjecture, originated in probability theory, is wel…
Non-commutative error correcting codes and proper subgroup testing
Michael Chapman, Irit Dinur, Alexander Lubotzky
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms wh…
Stability of Homomorphisms, Coverings and Cocycles II: Examples, Applications and Open problems
Michael Chapman, Alexander Lubotzky
Coboundary expansion (with coefficients), and variations on it, have been the focus of intensive research in the last two decades. It was used to study random comple…
Stability of Homomorphisms, Coverings and Cocycles I: Equivalence
Michael Chapman, Alexander Lubotzky
This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part…