In abstract algebra, an epigroup is a semigroup in which every element has a power that belongs to a subgroup.
More generally, in an arbitrary semigroup an element is called group-bound if it has a power that belongs to a subgroup.
[4] Epigroups were first studied by Douglas Munn in 1961, who called them pseudoinvertible.
[5] By analogy with periodic semigroups, an epigroup S is partitioned in classes given by its idempotents, which act as identities for each subgroup.
If an epigroup S has a partition in unipotent subepigroups (i.e. each containing a single idempotent), then this partition is unique, and its components are precisely the unipotency classes defined above; such an epigroup is called unipotently partionable.