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Hierarchies of Computable groups and the word problem1

Published online by Cambridge University Press:  12 March 2014

Frank B. Cannonito
Frank B. Cannonito*
Affiliation:
Hughes Aircraft Company, Fullerton, California
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 376 - 392
Copyright
Copyright © Association for Symbolic Logic 1996

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Footnotes

1

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.

References

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