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An algebraic characterization of groups with soluble word problem1

Published online by Cambridge University Press:  09 April 2009

William W. Boone  and
Graham Higman
William W. Boone
Affiliation:
University of Illinois, Urbana-Champaign, Illinois, U.S.A.
Graham Higman
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OXI, 3LB, England.
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The following theorem is the focal point of the present paper. It stipulates an algebraic condition equivalent, in any finitely generated group, to the solubility of the word problem.

THEOREM I. A necessary and sufficient condition that a finitely generated group G have a soluble word problem is that there exist a simple group H, and a finitely presented group K, such that G is a subgroup of H, and H is a subgroup of K.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 1 , August 1974 , pp. 41 - 53
Copyright
Copyright © Australian Mathematical Society 1974

References

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