Epigroups whose subepigroup lattice is 0-modular or 0-distributive. (Q1014267)

Let \(S\) be an epigroup, i.e., a semigroup in which some power of any element lies in a subgroup of \(S\). It is known that \(S\) can be regarded as a unitary semigroup with the unitary operation of pseudoinversion. Subsemigroups of \(S\) which are closed under this operation are just the subepigroups. A description of the epigroups named in the title is given.