Small Inherently Nonfinitely Based Finite Semigroups

We show how to construct all "forbidden divisors" for the pseudovaricty of not inherently nonfinitely based finite semigroups. Several other results concerning finite semigroups that generate an inherently nonfinitely based variety that is miminal amongst those generated by finite semigroups are obtained along the way. For example, aside from the variety generated by the well known six element Brandt monoid B1 2, a variety of this type is necessarily generated by a semigroup with at least 56 elements (all such semigroups with 56 elements are described by the main result).