Finitely generated lattice-ordered groups with soluble word problem
A. M. W. Glass · Journal of Group Theory · 2008
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.