A Note on the Definitions of Blocks of Epigroups

Abstract

A semigroup is called an epigroup if for any element in this semigroup some power of the element lies in the maximal subgroup of the given semigroup. In this paper two variants of definitions of blocks of semigroups are given and we prove that two of them turn out to coincide in the case of epigroups. We also offer the third definition of blocks of epigroups and show that if blocks of epigroups are subsemigroups, then this definition is equivalent to the other two.