Representing subalgebras as retracts of finite subdirect powers

Abstract

We prove that if $\mathbb{A}$ is an algebra that is supernilpotent with respect to the $2$-term higher commutator, and $\mathbb{B}$ is a subalgebra of $\mathbb{A}$, then $\mathbb{B}$ is representable as a retract of a finite subdirect power of $\mathbb{A}$.

13 pages. Keywords: abelian, formation, higher commutator, pseudovariety, supernilpotent, two term condition, unary algebra