Finite automata of polynomial growth do not generate a free group. (Q1768261)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Finite automata of polynomial growth do not generate a free group. |
scientific article; zbMATH DE number 2145817
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite automata of polynomial growth do not generate a free group. |
scientific article; zbMATH DE number 2145817 |
Statements
Finite automata of polynomial growth do not generate a free group. (English)
0 references
15 March 2005
0 references
In an earlier paper, the author conjectured that finite-state automata of polynomial growth cannot generate free groups of rank 2. In this paper, the author proves, under some natural hypotheses, that finite-state automorphisms of polynomial growth cannot generate free subgroups of rank 2 of the group of automorphisms of a regular rooted tree of arbitrary degree.
0 references
regular rooted trees
0 references
automorphisms of trees
0 references
finite automata
0 references
polynomial growth
0 references
free groups
0 references
0 references
