The Dehn function, word problem, and bounded word problem for finitely generated decidable group presentations

For finite group presentations, the word problem is solvable if and only if the Dehn function is computable. Additionally, the bounded word problem is always solvable. For finitely generated decidable group presentations, this is not always the case. The main result of the present work is to determine whether there exist examples of finitely generated decidable group presentations for each combination of solvability/unsolvability of the word problem, solvability/unsolvability of the bounded word problem, and computability/uncomputability of the Dehn function.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Cummins, Desmond

Contributors dc:contributor

• Ivanov, Sergei V.
• Kapovitch, Ilia
• Leininger, Christopher J.
• Schupp, Paul E.

• Group Theory
• Dehn Function
• Word Problem
• Bounded Word Problem

Statement dc:rights

• Copyright 2012 Desmond Cummins

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/34463

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/34463