33 citations · 63 across the 21 of their papers we have counts for
3 papers · 1 filter
Orbit automata as a new tool to attack the order problem in automaton groups
Ines Klimann, Matthieu Picantin, Dmytro Savchuk
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group on the subtrees corresponding to the orbits of on levels of the tree. T…
Ergodic decomposition of group actions on rooted trees
Rostislav Grigorchuk, Dmytro Savchuk
We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of erg…
A connected 3-state reversible Mealy automaton cannot generate an infinite Burnside group
Ines Klimann, Matthieu Picantin, Dmytro Savchuk
The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples.…