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math.GR2025
Finite dimensional amenable groups
Anna Erschler, Ivan Mitrofanov
We show that an amenable group of finite Assouad-Nagata dimension satisfies the property of Shalom. Such infinite groups are known to admit a virtual homomorphism onto $\m…
math.GR2018
On the existence of free subsemigroups in reversible automata semigroups
Dominik Francoeur, Ivan Mitrofanov
We prove that the semigroup generated by a reversible Mealy automaton contains a free subsemigroup of rank two if and only if it contains an element of infinite order.
math.GR2017
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…