Graham Higman proved that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. The analogue for lattice-ordered groups is considered here. Clearly, the finitely generated lattice-ordered groups that can be embedded in finitely presented lattice-ordered groups must have recursively enumerable sets of defining relations. The converse direction is proved for a special class of lattice-ordered groups.

Embedding finitely generated Abelian lattice-ordered groups : Higman's theorem and a realisation of \pi / A.M.W. Glass, V. Marra. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 68:3(2003 Dec), pp. 545-562.

### Embedding finitely generated Abelian lattice-ordered groups : Higman's theorem and a realisation of \pi

#### Abstract

Graham Higman proved that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. The analogue for lattice-ordered groups is considered here. Clearly, the finitely generated lattice-ordered groups that can be embedded in finitely presented lattice-ordered groups must have recursively enumerable sets of defining relations. The converse direction is proved for a special class of lattice-ordered groups.
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Lattice-ordered groups ; Higman's Theorem ; Recursive functions ; Polyhedral geometry
Settore MAT/02 - Algebra
Settore MAT/01 - Logica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/19767
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