Київський Вісник Київського національного університету імені Тараса Шевченка / Київський, університет імені національний; редкол.: голов. ред. Анісімов А.В. ; Хусаінов Д.Я., Arturs Medvids, Miklos Ronto [та ін.]. - Київ, 2016
Анотація:
Constructions of explicit examples of ? groups generated by automata are very important in modern geometric group theory. The full automorphism group of a regular rooted tree is rich of free subgroups. Thus groups of automata are naturally suitable for constructing free groups. A few approaches to construct faithful representations of free groups by automata are well-known. In this paper a new example of the free group of rank two generated by finite initial automata is described. Both these automata have four inner states and are considered over an alphabet with five letters. As a base of a following construction the automaton known as the adding machine over the binary alphabet was used. The proof allows one to construct explicitly a word that is not a fixed point of a given non-identity element of the free group.
