On linearly ordered subgroups of a lattice ordered group
On monotone permutations of -cyclically ordered sets
For an -cyclically ordered set with the -cyclic order let be the set of all monotone permutations on . We define a ternary relation on the set . Further, we define in a natural way a group operation (denoted by ) on . We prove that if the -cyclic order is complete and , then is a half cyclically ordered group.
On orderability of topological groups.
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 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 some types of kernels of a convergence -group
On some varieties of weakly associative lattice groups
On summability in convergence -groups
On the affine completeness of lattice ordered groups
In the paper it is proved that a nontrivial direct product of lattice ordered groups is never affine complete.
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 extension of positive operators
On the extension of subadditive measures in lattice ordered groups
A lattice ordered group valued subadditive measure is extended from an algebra of subsets of a set to a -algebra.
On the Jakubík Problem on radical classes of lattice ordered groups
On the lattice of semisimple classes of linearly ordered groups
On the lattice of torsion classes of lattice ordered groups
On the maximal Dedekind completion of a half partially ordered group
On the maximal Dedekind completion of a lattice ordered group