An algebraic characterization of groups with soluble word problem-Reference-Cited by-同舟云学术

An algebraic characterization of groups with soluble word problem

Published:1974-08 Issue:1 Volume:18 Page:41-53
ISSN:0004-9735
Container-title:Journal of the Australian Mathematical Society
language:en
Short-container-title:J. Aust. Math. Soc.

Author:

Boone William W.,Higman Graham

Abstract

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.

Publisher

Cambridge University Press (CUP)

Reference17 articles.

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2. [12] McKenzie R. and Thompson R. J. , ‘Unsolvable word problems’, 457–478 of Word problems: decision problems and the Burnside problem in group theory. Publication data are above in reference [1].

3. Subgroups of finitely presented groups

4. [8] Fridman A. A. , Degrees of unsolubility of the problem of identity in finitely presented groups (in Russian), Izdalel'sto ‘Nauka’, Moscow 1967, 193.

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