On Properties of Relatively Hyperbolic Groups

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Creator: 

Zhang, Ming Ming

Date: 

2018

Abstract: 

We discuss a number of problems in relatively hyperbolic groups. We show that the word problem and the conjugacy (search) problem are solvable in linear and quadratic time, respectively, for a relatively hyperbolic group, whenever the corresponding problem is solvable in linear and quadratic time in each parabolic subgroup. We also consider the class of finitely generated toral relatively hyperbolic groups. We show that groups from R are commutative transitive and generalize a theorem proved by Benjamin Baumslag to R. Moreover, we discuss two definitions of (fully) residually-C groups and prove the equivalence of the two definitions for C=R. Let Γ ∈ R . We prove that every finitely generated fully residually-Γ group embeds into a group from R. On the other hand, we give an example of a finitely generated torsion-free fully residually-H group that does not embed into a group from R; H is the class of hyperbolic groups.

Subject: 

Education - Mathematics

Language: 

English

Publisher: 

Carleton University

Thesis Degree Name: 

Doctor of Philosophy: 
Ph.D.

Thesis Degree Level: 

Doctoral

Thesis Degree Discipline: 

Pure Mathematics

Parent Collection: 

Theses and Dissertations

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