A Study on Essentially Minimal Clones

For a non-empty set A, a clone C on A is essentially minimal if C is not a minimal clone and is minimal among all clones on A containing essential functions. For a finite A with |A|=A Study on Essentially Minimal Clones (>2), we prove that any essentially minimal clone on A has a generator whose arity is no greater than κ. We also determine all conjugate classes of essentially minimal groupoids on a three-element set.