The concept of self-similar automata over a changing alphabet and lamplighter groups generated by such automata

Abstract

Generalizing the idea of self-similar groups defined by Mealy automata, we itroduce the notion of a self-similar automaton and a self-similar group over a changing alphabet. We show that every finitely generated residually-finite group is self-similar over an arbitrary unbounded changing alphabet. We construct some naturally defined self-similar automaton representations over an unbounded changing alphabet for any lamplighter group $K\wr \mathbb{Z}$ with an arbitrary finitely generated (finite or infinite) abelian group $K$.

References in corpus (1)

• The concept of duality for automata over a changing alphabet and generation of a free group by such automata

Cited by in corpus (2)

• On groups generated by bi-reversible automata: the two-state case over a changing alphabet
• The classification of abelian groups generated by time-varying automata and by Mealy automata over the binary alphabet