Finitely generated latticeordered groups with soluble word problem
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 latticeordered groups: Theorem: A finitely generated latticeordered group has soluble word problem if and only if it can be embedded in an simple latticeordered group that can be embedded in a finitely presented latticeordered group. The proof uses permutation groups and the ideas used to prove the latticeordered group analogue of Higman's Embedding Theorem.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1699
 Bibcode:
 2007arXiv0710.1699G
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Logic