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EPIGROUP

Epigroup

Type of semigroup

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

Epigroup

Completely regular semigroup

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

Completely regular semigroup

Completely_regular_semigroup

Special classes of semigroups

Families of certain algebraic structures

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

Special classes of semigroups

Special_classes_of_semigroups

Green's relations

and J are the same; this is also the case in a rational monoid or in an epigroup. There is also a formulation of D in terms of equivalence classes, derived

Green's relations

Green's_relations

Cancellative semigroup

Semigroup with the cancellation property

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

Cancellative semigroup

Cancellative_semigroup

Monogenic semigroup

Semigroup generated by a single element

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

Monogenic semigroup

Monogenic_semigroup

Nambooripad order

Mathematical group

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

Nambooripad order

Nambooripad_order