  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 embedded in an simple
lattice-ordered group that can be embedded in a finitely presented
lattice-ordered group. The proof uses permutation groups and the ideas used to
prove the lattice-ordered group analogue of Higman's Embedding Theorem.
