A combinatorial property of logical algebras

Logic gives a technique for the articial intelligence to make the computers simulate human being in dealing with certainty and uncertainty in information. Various logical algebras have been proposed and researched as the semantical  systems of non-classical logical systems. In this paper using the concept of commutator, we introduce the Engel algebra and then study a condition on infinite subsets of infinite algebras. We also show that some logical algebras satisfy to this condition but do not have the properties associated with that condition.