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The closed subgroup problem for lattice-ordered groups. (English) Zbl 0682.06011
Kenoyer gave two examples proving that in the lattice of convex \(\ell\)- subgroups of a lattice-ordered group it was impossible to distinguish the closed convex \(\ell\)-subgroups. However, one of his examples was non- normal-valued. Here the same question is recast for normal-valued \(\ell\)- groups, and it remains open. The main theorem gives an interesting class of \(\ell\)-groups in which closed convex \(\ell\)-subgroups can be recognized in the lattice of convex \(\ell\)-subgroups.
Reviewer: J.Martinez

MSC:
06F15 Ordered groups
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