Article citationsMore>>

Rhemtulla, A. and Rolfsen, D. (2002) Local Indicability in Ordered Groups: Braids and Elementary Amenable Groups. Proceedings of the American Mathematical Society, 30, 2569-2577.
https://doi.org/10.1090/S0002-9939-02-06413-4

has been cited by the following article:

• TITLE: The Class of Orderable Groups Is a Quasi-Variety with Undecidable Theory

  AUTHORS: Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, Dennis Spellman

  KEYWORDS: Orderable Group, Left Orderable Group, Quasi-Variety

  JOURNAL NAME: Advances in Pure Mathematics, Vol.11 No.3, March 29, 2021

  ABSTRACT: Let G be a group. G is right-orderable provided it admits a total order ≤ satisfying hg1 ≤ hg2 whenever g1 ≤ g2. G is orderable provided it admits a total order ≤ satisfying both: hg1 ≤ hg2 whenever g1 ≤ g2 and g1h ≤ g2h whenever g1 ≤ g2. A classical result shows that free groups are orderable. In this paper, we prove that left-orderable groups and orderable groups are quasivarieties of groups both with undecidable theory. For orderable groups, we find an explicit set of universal axioms.