On convex subgroups of groups with the interpolation property

Characteristics of groups with the interpolation relation (not necessarily directed) are considered. A necessary and sufficient condition for a partially ordered group to be an interpolation group is obtained. An almost orthogonality criterion for positive elements of an interpolation group is proved. Characteristics of minimal convex directed subgroups containing almost orthogonal elements are described. Properties of convex directed subgroups in the subclass of interpolation groups in which each element is a quotient of two almost orthogonal elements are investigated.