AbstractThe notion of torsion radical of cyclically ordered groups is defined analogously as in the case of lattice ordered groups. We denote by T the collection of all torsion radicals of cyclically ordered groups. For τ1, τ2 ∈ T, we put τ1 ∈ τ2 if τ1(G) □ τ2(G) for each cyclically ordered group G. We show that T is a proper class; nevertheless, we apply for T the usual terminology of the theory of partially ordered sets. We prove that T is a complete completely distributive lattice. The analogous result fails to be valid for torsion radicals of lattice ordered groups. Further, we deal with products of torsion classes of cyclically ordered groups.
