isomorfklasser

In mathematics, an isomorfklasser, or isomorphism class, refers to a collection of mathematical objects that are structurally identical. Objects within the same isomorfklasser can be transformed into one another through an isomorphism, which is a bijective (one-to-one and onto) mapping that preserves the relevant structure of the objects. The specific structure being preserved depends on the mathematical context, such as algebraic operations in group theory or the adjacency relationships in graph theory. Essentially, two objects belong to the same isomorfklasser if, for all practical purposes, they behave in the same way with respect to the defining operations or relations. This concept is fundamental for classifying and understanding mathematical structures by identifying those that are indistinguishable from a structural viewpoint. For example, in group theory, all cyclic groups of order n are in the same isomorfklasser.