Completely regular semigroup

Definition
A completely regular semigroup is a semigroup (i.e., a set with associative binary operation) where the subsemigroup generated by any element is a group under the induced multiplication.

Note that the identity elements for these groups need not, in general, coincide. If they do coincide, then the completely regular semigroup is a group.

Stronger properties

 * Weaker than::Group
 * Weaker than::Clifford semigroup

Weaker properties

 * Stronger than::Regular semigroup
 * Stronger than::Epigroup
 * Stronger than::Eventually regular semigroup

Incomparable properties

 * Inverse semigroup