MAL’TSEV CONDITIONS, LACK OF ABSORPTION, AND SOLVABILITY

Abstract. We provide a new characterization of several Mal’tsev conditions for locally finite varieties using hereditary term properties. We show a particular example how lack of absorption causes collapse in the Mal’tsev hierarchy, and point out a connection between solvability and lack of absorption. As a consequence, we provide a new and conceptually simple proof of a result of Hobby and McKenzie, saying that locally finite varieties with a Taylor term possess a term which is Mal’tsev on blocks of every solvable congruence in every finite algebra in the variety. 1