On Identity Bases of Epigroup Varieties

Let C n and C n be the varieties of all completely regular and of all completely simple semigroups, respectively, whose idempotent generated subsemigroups are periodic with period n. We use Olʹshanski ʹs theory of geometric group presentations to show that for large odd n these varieties (and similarly defined varieties of epigroups) do not have finitely axiomatizable equational theories.