Unconditional Grün's lemma for perfect semiassociative Mal'cev algebras

Determine which perfect semiassociative Mal'cev algebras satisfy an unconditional Grün's lemma, meaning that their second-center coincides with their center.

Background

The paper proves a conditional Grün's lemma for all semiassociative Mal'cev algebras: for a perfect algebra, equality of the center and second-center is characterized by identities involving selected binary absorbing polynomials. Groups and multiplicative Lie algebras are shown to satisfy the unconditional result, whereas skew braces provide counterexamples. The open problem asks for a general classification or characterization of the perfect semiassociative Mal'cev algebras for which the conditional criterion is automatically satisfied.