The O'Nan–Scott theorem

The O'Nan–Scott theorem is a mathematical result that classifies highly symmetrical structures called primitive permutation groups. These groups are ways of organizing elements so that the structure looks the same from many different perspectives. The theorem breaks down these complex groups into simpler, well-understood types based on how they act on sets, dividing them into categories like those involving simple building blocks or specific symmetries. This classification helps mathematicians understand the fundamental nature of symmetry and permutation actions in various mathematical and scientific contexts.