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Abstract
William W. Boone and Graham Higman proved that a finitely generated group has soluble word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group. We prove the exact analogue for lattice-ordered groups:
Theorem.A finitely generated lattice-ordered group has soluble word problem if and only if it can be ℓ-embedded in an ℓ-simple lattice-ordered group that can be ℓ-embedded in a finitely presented lattice-ordered group.
The proof uses permutation groups, a technique of Holland and McCleary, and the ideas used to prove the lattice-ordered group analogue of Higman's embedding theorem.
Received: 2007-03-19
Published Online: 2008-02-22
Published in Print: 2008-01-01
© Walter de Gruyter