46 citations · 232 across the 47 of their papers we have counts for
10 papers · 1 filter
Invariant subsets of the space of subgroups, equational compactness and the weak equivalence of actions
Gabor Elek, Konrad Krolicki
Equationally compact subgroups of countable groups were introduced by Banaschewski. For all known cases the orbit closure of such a subgroup is a countable subset in the space of s…
Full groups and soficity
Gabor Elek
First, we answer a question of Pestov, by proving that the full group of a sofic equivalence relation is a sofic group. Then, we give a short proof of the theorem of Grigorchuk and…
Hyperfinite actions on countable sets and probability measure spaces
Miklos Abert, Gabor Elek
We introduce the notion of hyperfiniteness for permutation actions of countable groups on countable sets and give a geometric and analytic characterization, similar to the known ch…
Sofic representations of amenable groups
Gabor Elek, Endre Szabo
Using probabilistic methods, Collins and Dykema proved that the free product of two sofic groups amalgamated over a monotileably amenable subgroup is sofic as well. We show that th…
Dynamical properties of profinite actions
Miklós Abért, Gábor Elek
We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and onl…
Non-abelian free groups admit non-essentially free actions on rooted trees
Miklos Abert, Gabor Elek
We show that every countable non-abelian free group admits a spherically transitive action on a rooted tree such that the action of on the boundary of is not essent…