Finite Automata of Polynomial Growth do Not Generate A Free Group

By Said Najati Sidki. 2004

53 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3c20956edfd1d6dafb21addc5d71b1ca96763267

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Rostislav I. Grigorchuk
2. Volodymyr V. Nekrashevych
3. Zoran Sunic
4. Ievgen V. Bondarenko
5. Yevgen Muntyan
6. Dmytro Savchuk
7. Rostyslav V. Kravchenko
8. Miklós Abért

In Geometry and Topology

1. Rostislav I. Grigorchuk
2. Volodymyr V. Nekrashevych
3. Zoran Sunic
4. Ievgen V. Bondarenko
5. Yevgen Muntyan
6. Dmytro Savchuk
7. Rostyslav V. Kravchenko
8. Enrique Pardo

In Mathematical Physics

1. Rostislav I. Grigorchuk
2. Zoran Sunic
3. Volodymyr V. Nekrashevych
4. Ievgen V. Bondarenko
5. Yaroslav Vorobets
6. Enrique Pardo
7. R. Exel
8. Laurent Bartholdi

Citations in the corpus

• Classification of groups generated by 3-state automata over a 2-letter alphabet (2008, background): “plighter group are given by a= σ(1,a) a= σ(b,a) a= (b,a) 1 = (1,1) b= (b,a), b= σ(a,b) (7) respectively. The class of polynomially growing automata was introduced by Sidki in [Sid00]. Sidki proved in [Sid04] that no group generated by such an automaton contains free subgroups of rank 2. As we alread”
• Groups St Andrews 2005: Self-similarity and branching in group theory (2007, background): “Groups of polynomial growth do not have free subgroups (Sidki [8]).”