Epigroup

Definition
An epigroup (also termed a group-bound semigroup) is a semigroup with the property that every element has a power, such that the subsemigroup generated by that power, is a subgroup (i.e., a group under the induced multiplication).

Stronger properties

 * Weaker than::Clifford semigroup
 * Weaker than::Completely regular semigroup

Weaker properties

 * Stronger than::Eventually regular semigroup