The Dehn function, word problem, and bounded word problem for finitely generated decidable group presentations
Cummins, Desmond
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https://hdl.handle.net/2142/34463
Description
Title
The Dehn function, word problem, and bounded word problem for finitely generated decidable group presentations
Author(s)
Cummins, Desmond
Issue Date
2012-09-18T21:18:24Z
Director of Research (if dissertation) or Advisor (if thesis)
Ivanov, Sergei V.
Doctoral Committee Chair(s)
Kapovitch, Ilia
Committee Member(s)
Ivanov, Sergei V.
Leininger, Christopher J.
Schupp, Paul E.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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