On adjoining units to hyper-archimedean -groups
On convexities of -groups
On embedding properties of -groups.
On half lattice ordered groups
On lexico extensions of lattice ordered groups
On linearly ordered subgroups of a lattice ordered group
On ordering the groups with nilpotent commutant.
On orthogonally -complete lattice ordered groups
In this paper we prove a theorem of Cantor-Bernstein type for orthogonally -complete lattice ordered groups.
On radical classes of Abelian linearly ordered groups
On some completeness properties for lattice ordered groups
On some interpolation rules for lattice ordered groups
Let be an infinite cardinal. In this paper we define an interpolation rule for lattice ordered groups. We denote by the class of all lattice ordered groups satisfying , and prove that is a radical class.
On the completion of cyclically ordered groups
On the dynamics of (left) orderable groups
We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable torsion-free nilpotent groups which are not rank-one Abelian. Finally, we apply our methods to the case of braid...
On the Jakubík Problem on radical classes of lattice ordered groups
Orderable 3-manifold groups
We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact -irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds’ groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question of virtual orderability...