Invariant relations in a finite domain

ABSTRACT: Some results of an abstract inquiry into the concept of invariance are presented. The objects to be judged in their possible invariance are relations of arbitrary degrees in one single domain, when they are represented as sets of strings of elements in that domain. The domain itself is presumed to be of finite size, and the transformations with respect to which invariance is judged are injective functions between parts of it. The study focuses on correspondences between algebraic structures of possible relations and algebraic structures of possible transformations, as they are dually interrelated through the invariance condition.