In this note we prove a selection of commutativity theorems for various classes of semigroups. For instance, if in a separative or completely regular semigroup we have and for all where and are relatively prime, then is commutative. In a separative or inverse semigroup , if there exist three consecutive integers such that for all , then is commutative. Finally, if is a separative or inverse semigroup satisfying for all , and if the cubing map is injective, then is commutative.
Cite this article
Francisco Araújo, Michael Kinyon, Commutativity theorems for groups and semigroups. Port. Math. 74 (2017), no. 3, pp. 243–255DOI 10.4171/PM/2005