Finitely generated lattice-ordered groups with soluble word problem

Details Finitely generated lattice-ordered groups with soluble word problem Finitely generated lattice-ordered groups with soluble word problem

2007-10-09

arxiv.org/abs/0710.1699v1

Mathematics

Group Theory

Scientific paper

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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