8 papers · 1 filter
Centralizers of sofic approximations of Kazhdan groups
Vadim Alekseev, Andreas Thom
We prove that a Kazhdan group admitting a sofic embedding into a metric ultraproduct of symmetric groups with a centralizer that acts ergodically on the associated Loeb probability…
On the Howe--Moore property for automorphism groups of buildings
Andreas Thom, Pierre-Emmanuel Caprace
Let be a closed type-preserving subgroup of the automorphism group of a thick locally finite building of finite rank, and assume that acts Weyl-transitively. We prove t…
On non-isomorphic universal sofic groups
Vadim Alekseev, Andreas Thom
We show that there are non-isomorphic universal sofic groups. This proves a conjecture of Simon Thomas.
On the asymptotic equidistribution of word values in symmetric groups
Vadim Alekseev, Jakob Schneider, Andreas Thom
We prove an asymptotic equidistribution result for word values for words with constants in the symmetric group. We also speculate about simultaneous asymptotic equidistribution res…
Cubic maps from the group of order
Vadim Alekseev, Andreas Thom
The purpose of this note is to classify unital cubic maps from the cyclic group of order into an arbitrary non-abelian group. We show that the universal group admitting a unita…
Remarks on approximability and stability for groups
Vadim Alekseev, Andreas Thom
In this paper, we provide several instances in which interesting approximation and stability properties are inherited by quotients with respect to finitely generated normal subgrou…