<prompt> Passage: Finite symmetry groups such as the Mathieu groups are used in coding theory, which is in turn applied in error correction of transmitted data, and in CD players. Maombi mengine ni tofauti Galois nadharia, ambayo sifa kazi kuwa antiderivatives ya fomu iliyowekwa, kutoa kundi-theoretic vigezo kwa ajili ya wakati ufumbuzi wa baadhi differential equations ni well-behaved. Geometric mali kwamba kubaki imara chini ya kundi vitendo ni kuchunguzwa katika jiometri invariant nadharia. Swali: Ni aina gani ya kundi ni Mathieu makundi?  <response>: Makundi ya usawa wa mwisho 