Equations in Self-Similar Groups

von Thorsten Groth
Dissertation
Datum der mündl. Prüfung:2018-02-06
Erschienen:2018-02-16
Betreuer:Prof. Dr. Laurent Bartholdi
Gutachter:Prof. Dr. Laurent Bartholdi
Gutachter:Dr. Vadim Alekseev
Zum Verlinken/Zitieren: http://dx.doi.org/10.53846/goediss-6728

 

 

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Zusammenfassung

Englisch

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
 
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