“Groups are important because they arise from structures as systems of automorphisms of those structures . . . Group tables and group diagrams are devices to make groups explicit or to visualise them, but they are utterly inefficient tools to introduce groups or to prove that some system is a group ... Are there valid arguments to teach a school group theory, different from the genuine one? I would doubt it.” H. FREUDENTHAL: Address to the ICME congress at Exeter, 1972, on What groups mean in mathematics, and what they should mean in mathematical education.