140 citations · 1.3k across the 89 of their papers we have counts for
4 papers · 1 filter
The word and order problems for self-similar and automata groups
Laurent Bartholdi, Ivan Mitrofanov
We prove that the word problem is undecidable in functionally recursive groups, and that the order problem is undecidable in automata groups, even under the assumption that they ar…
Commutator width in the first Grigorchuk group
Laurent Bartholdi, Thorsten Groth, Igor Lysenok
Let be the first Grigorchuk group. We show that the commutator width of is : every element is a product of two commutators, and also of six conjugates of $a…
Decidability problems in automaton semigroups
Laurent Bartholdi
We consider decidability problems in self-similar semigroups, and in particular in semigroups of automatic transformations of . We describe algorithms answering the word probl…
Amenability of groups and -sets
Laurent Bartholdi
This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of…