Bludov, V. V.; Glass, A. M. W.; Rhemtulla, Akbar H. Ordered groups in which all convex jumps are central. (English) Zbl 1031.20036 J. Korean Math. Soc. 40, No. 2, 225-239 (2003). A linearly ordered group \(G\) is centrally ordered if \([G,D]\subseteq C\) for every convex jump \(C\prec D\) in \(G\) or equivalently, if \(f^{-1}gf\leq f^2\) for all \(f,g\) with \(g>1\). It is proved that if every order on every two-generator subgroup of a locally soluble orderable group is central, then \(G\) is locally nilpotent. An example of a non-nilpotent two-generator metabelian orderable group in which all orders are central is constructed. Reviewer: Nikolai Yakovlevich Medvedev (Barnaul) Cited in 4 Documents MSC: 20F60 Ordered groups (group-theoretic aspects) 06F15 Ordered groups 20F19 Generalizations of solvable and nilpotent groups 20F14 Derived series, central series, and generalizations for groups 20E26 Residual properties and generalizations; residually finite groups Keywords:locally soluble groups; locally nilpotent groups; linearly ordered groups; convex jumps; central series; centrally ordered groups PDFBibTeX XMLCite \textit{V. V. Bludov} et al., J. Korean Math. Soc. 40, No. 2, 225--239 (2003; Zbl 1031.20036) Full Text: DOI