| The study of CT-groups, i.e., groups in which commutativity is a transitive relation, dates back to Weisner (1925) and Suzuki (1957). Weisner showed that a finite CT-group is either solvable or simple. Subsequently, Suzuki proved that finite simple CT-groups are projective special linear groups over finite fields of characteristic 2. I will present my work on the complete classification of locally finite CT-groups. Other topics include some types of torsion-free solvable CT-groups and an application to discriminating groups. |