The Largest Group Contained in the Order Completion of a Totally Ordered Group


For a totally ordered group G we determine the largest group contained in its Dedekind completion G#. It was the result of studying the family of convex subgroups of G and some well-known properties of ordered groups.

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Correspondence to Adrialy Muci or Elena Olivos.

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The text was submitted by the authors in English.

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Muci, A., Olivos, E. The Largest Group Contained in the Order Completion of a Totally Ordered Group. P-Adic Num Ultrametr Anal Appl 12, 123–133 (2020).

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Key words

  • Dedekind completion
  • totally ordered group
  • convex subgroups