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

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Title: The Dehn function, word problem, and bounded word problem for finitely generated decidable group presentations
Author(s): Cummins, Desmond
Director of Research: Ivanov, Sergei
Doctoral Committee Chair(s): Kapovich, Ilya
Doctoral Committee Member(s): Ivanov, Sergei; Leininger, Christopher; Schupp, Paul
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Group Theory Dehn Function Word Problem Bounded Word Problem
Abstract: 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.
Issue Date: 2012-09-18
URI: http://hdl.handle.net/2142/34463
Rights Information: Copyright 2012 Desmond Cummins
Date Available in IDEALS: 2012-09-18
Date Deposited: 2012-08
 

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