The Automaton Realization of Iterated Wreath Products of Cyclic Groups

Abstract

We study profinite groups which are infinitely iterated wreath products W _∞ = …≀C _{n 2} ≀C _{n 1} of finite cyclic groups via combinatorial language of transducers. Namely, we provide a naturally defined automaton realization of the group W _∞ by an automaton over a changing alphabet. Our construction gives a characterization of these profinite groups as automaton groups, i.e. as groups generated by a single automaton.

Key Words:

• Automaton
• Automorphisms of rooted trees
• Group generated by an automaton
• Iterated wreath product

2010 Mathematics Subject Classification:

• 20F05
• 20E22
• 20E18
• 20E08
• 68Q45

Notes

Communicated by S. Hermiller.