83 citations · 319 across the 28 of their papers we have counts for
4 papers · 2 filters
Scale-invariant groups
Volodymyr Nekrashevych, Gábor Pete
Motivated by the renormalization method in statistical physics, Itai Benjamini defined a finitely generated infinite group G to be scale-invariant if there is a nested sequence of…
Classification of groups generated by 3-state automata over a 2-letter alphabet
Ievgen Bondarenko, Rostislav Grigorchuk, Rostyslav Kravchenko +4
This article contains most of the known results on the classification of groups generated by 3-state automata over a 2-letter alphabet, extending the previous papers 0704.3876 and…
On amenability of automata groups
Laurent Bartholdi, Vadim A. Kaimanovich, Volodymyr V. Nekrashevych
We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The pr…
Free subgroups in groups acting on rooted trees
Volodymyr Nekrashevych
We show that if a group acting faithfully on a rooted tree has a free subgroup, then either there exists a point of the boundary and a free subgroup of …