Finitely generated lattice-ordered groups with soluble word problem
Group Theory
2007-10-10 v1 Logic
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 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.
Cite
@article{arxiv.0710.1699,
title = {Finitely generated lattice-ordered groups with soluble word problem},
author = {A. M. W. Glass},
journal= {arXiv preprint arXiv:0710.1699},
year = {2007}
}