Equations in Self-Similar Groups

by Thorsten Groth
Doctoral thesis
Date of Examination:2018-02-06
Date of issue:2018-02-16
Advisor:Prof. Dr. Laurent Bartholdi
Referee:Prof. Dr. Laurent Bartholdi
Referee:Dr. Vadim Alekseev
Persistent Address: http://dx.doi.org/10.53846/goediss-6728

 

 

Files in this item

Name:equations.pdf
Size:1.27Mb
Format:PDF

The following license files are associated with this item:

Abstract

English

We introduce a method on how to decide solvebility of quadratic equations in self-similar groups and use this method to show that certain equations always have a solution. In particular the group of tree automorphisms and the Neumann-Segal groups have commutator witdth one. The Grigorchuk group and the Gupta Sidki group have commutator width at most two.
Keywords: Self-Similar; Automaton group; Mealy machine; quadratic equation; Grigorchuk group; Neumann-Segal group; Commutator width
 
Statistik