Groups in Which Commutativity Is a Transitive Relation

We investigate the structure of groups in which commutativity is a transitive relation on non-identity elements (CT-groups). A detailed study of locally finite, polycyclic, and torsion-free solvableCT-groups is carried out. Other topics include fixed-point-free groups of automorphisms of abelian torsion groups and their cohomology groups.