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Hierarchies of Computable groups and the word problem1
Published online by Cambridge University Press: 12 March 2014
Extract
The word problem for groups was first formulated by M. Dehn [1], who gave a solution for the fundamental groups of a closed orientable surface of genus g ≧ 2. In the following years solutions were given, for example, for groups with one defining relator [2], free groups, free products of groups with a solvable word problem and, in certain cases, free products of groups with amalgamated subgroups [3], [4], [5]. During the period 1953–1957, it was shown independently by Novikov and Boone that the word problem for groups is recursively undecidable [6], [7]; granting Church's Thesis [8], their work implies that the word problem for groups is effectively undecidable.
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- Research Article
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- Copyright © Association for Symbolic Logic 1996
Footnotes
This work was supported by the Air Force Systems Command, Research and Technology Division, Rome Air Development Center, Griffiss Air Force Base, New York, 13442, under contract AF 30(602)-3339, and forms a portion of the author's doctoral dissertation at Adelphi University.
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