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Ordering \(\text{BS}(1,3)\) using the Magnus transformation. (English) Zbl 1172.20031
Summary: Following a similar treatment of the Baumslag-Solitar group \(\text{BS}(1,2)\) by P. Bahls, [Commun. Algebra 35, No. 12, 4088-4095 (2007; Zbl 1170.20026)], we modify a transformation developed by Magnus to linearly order the group \(\text{BS}(1,3)\) given by the presentation \(\langle a,b\mid ab=ba^3\rangle\). We demonstrate how this same method will fail to admit such a treatment of the groups \(\text{BS}(1,n)\), \(n\geq 4\).
MSC:
20F60 Ordered groups (group-theoretic aspects)
20F05 Generators, relations, and presentations of groups
20M05 Free semigroups, generators and relations, word problems
06F05 Ordered semigroups and monoids
Citations:
Zbl 1170.20026
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