Epigroups

Abstract

An epigroup is a semigroup in which some power of any element lies in a subgroup of the given semigroup. The class of epigroups includes a number of important classes of semigroups. Not only some particular types of epigroups but epigroups as such can serve as the subject matter of a substantial theory. In this survey the following topics concerning epigroups are considered: epigroups as unary semigroups, certain “nice” decompositions, finiteness conditions.