The class of completely regular semigroups forms an important subclass of the class of regular semigroups, the class of inverse semigroups being another such subclass.
[5] In a completely regular semigroup, each Green H-class is a group and the semigroup is the union of these groups.
[6] Hence completely regular semigroups are also referred to as "unions of groups".
Epigroups generalize this notion and their class includes all completely regular semigroups.
"While there is an abundance of natural examples of inverse semigroups, for completely regular semigroups the examples (beyond completely simple semigroups) are mostly artificially constructed: the minimum ideal of a finite semigroup is completely simple, and the various relatively free completely regular semigroups are the other more or less natural examples.