On the minimal extension of the sequence $ \langle 0,1,1,7 \rangle $

Abstract.

This note shows that the p _n -sequence $\langle 0,1,1,7 \rangle$ has the minimal extension property in the class of algebras with a nonassociative binary operation. This generalizes the result of J. Galuszka and gives a partial solution of problem 18 raised by G. Grätzer and A. Kisielewicz of whether $\langle 0,1,1,7 \rangle$ has the minimal extension property. This result reduces the problem to the class of algebras with a semilattice operation.