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arXiv · 0710.1699

Finitely generated lattice-ordered groups with soluble word problem

A. M. W. Glass
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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 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.

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A. M. W. Glass. 2007-10-09. Finitely generated lattice-ordered groups with soluble word problem. https://arxiv.org/abs/0710.1699

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