The study of (non-abelian) finite simple groups can be traced back at least as far as Galois, who around 1830 understood their fundamental significance as obstacles to the solution of polynomial equations by radicals (square roots, cube roots, etc.). From the very beginning, Galois realised the importance of classifying the finite simple groups, and knew that the alternating groups A n are simple for n≥5, and he constructed (at least) the simple groups PSL2(p) for primes p≥5.
KeywordsNormal Subgroup Conjugacy Class Simple Group Maximal Subgroup Composition Factor
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