One -variable equations in torsion -free hyperbolic groups.

Title: One -variable equations in torsion -free hyperbolic groups.
Identifier: AAI3103129
identifier: 3103129
Creator: Kvaschuk, Alexei.
Contributor: Adviser: Alexei Miasnikov
Date: 2003
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Let G be a torsion-free hyperbolic group. The main result of this thesis describes the solution sets of one-variable equations in G. It turns out that every such solution set is given by a finite set of parametric solutions of the form falpha g, falphag betah, or falpha gf-alphah for some f, g, h ∈ G when parameters alpha and beta run over Z . In addition, an algorithm for finding these parametric words is given. This algorithm is based on the Big Powers ( BP ) property of hyperbolic groups. The second part of the thesis contains some general results on the class CBP of groups satisfying BP condition. We show that the class CBP is closed under free products with amalgamation and HNN-extensions provided the amalgamated (associated) subgroups satisfy some very natural conditions.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.