A Class of Two Generated Automaton Groups on a Three Letter Alphabet

a class of two generated automaton groups on a three letter alphabet

An automaton group: a computational case study

We introduce a two generated weakly branch contracting automaton group $G$ which is generated by a two state automaton on a three letter alphabet. Using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. Furthermore some algebraic properties of $G$ are detected .

Decomposition theorem for invertible substitutions on three - letter alphabet ∗

We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite set S of invertible substitutions such that any invertible substitution can be written as Iw ◦ σ1 ◦ σ2 ◦ · · · ◦ σk, where Iw is the inner automorphism associated with w, and σj ∈ S for 1 ≤ j ≤ k. As a consequence, M is the matrix of an invertible substitution if and only if it is a f...

an automaton group: a computational case study

we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .

Subgroups of Mapping Class Groups Generated by Three Dehn Twists

It has been shown that the mapping class group of a genus g ≥ 2 closed surface can be generated by 2g + 1 Dehn twists. Little is known, however, about the structure of those mapping class groups. This paper is an attempt to explain the structure of subgroups of the mapping class group of a closed surface of genus g ≥ 2 which are generated by three Dehn twists. 1 Background and Notation This pap...

The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable

We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy automata and to the decidability of freeness for semigroups generated by two-letter invertible-reversible Mealy automata.