In abstract algebra, an epigroup is a semigroup in which every element has a power that belongs to a subgroup. Formally, for all x in a semigroup S, there...

a) such that akxak = ak. Edwa Shum Higg p. 49 Quasi-periodic semigroup, epigroup, group-bound semigroup, completely (or strongly) π-regular semigroup, and...

rational monoid.[clarification needed] Furthermore they also coincide in any epigroup. There is also a formulation of D in terms of equivalence classes, derived...

completely regular semigroups are also referred to as "unions of groups". Epigroups generalize this notion and their class includes all completely regular...

S. Thus S must necessarily be a group. Furthermore, every cancellative epigroup is also a group. A commutative semigroup can be embedded in a group (i...

class is that of quasi-periodic semigroups (aka group-bound semigroups or epigroups) in which every element of the semigroup has a power that lies in a subgroup...

bs. In general, for an arbitrary semigroup ≤J is a subset of ≤M. For epigroups however, they coincide. Furthermore, if b is a regular element of S (which...