When is a right orderable group locally indicable?
Patrizia Longobardi, Mercede Maj, A. H. Rhemtulla · Proceedings of the American Mathematical Society · 1999
If a group G G has an ascending series 1 = G 0 ≤ G 1 ≤ ⋯ ≤ G ρ = G 1 = G_{0} \leq G_{1} \leq \dots \leq G_{\rho } = G of subgroups such that for each ordinal α , G α ⊲ G \alpha , G_{\alpha }\vartriangleleft G , and G α + 1 / G α G_{\alpha + 1}/G_{\alpha } has no non-abelian free subsemigroup, then G G is right orderable if and only if it is locally indicable. In particular if G G is a radical-by-periodic group, then it is right orderable if and only if it is locally indicable.