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Finite simple groups. --- Simple groups, Finite --- Finite groups --- Linear algebraic groups --- Group theory --- Finite simple groups

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Finite simple groups --- Congresses --- 512 --- -Simple groups, Finite --- Finite groups --- Linear algebraic groups --- Algebra --- Congresses. --- -Algebra --- 512 Algebra --- -512 Algebra --- Simple groups, Finite --- Groupes finis. --- Groupes simples finis --- Groupes, Théorie des --- Groupes, Théorie des

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Finite simple groups --- 512.54 --- Simple groups, Finite --- Finite groups --- Linear algebraic groups --- 512.54 Groups. Group theory --- Groups. Group theory --- Group theory

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Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. But gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Secondly, since each of them is in a sense recording some exceptional symmetry in spaces of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure. Motivated by initial results which showed that the Mathieu groups can be generated by highly symmetrical sets of elements, which themselves have a natural geometric definition, the author develops from scratch the notion of symmetric generation. He exploits this technique by using it to define and construct many of the sporadic simple groups including all the Janko groups and the Higman-Sims group. For researchers and postgraduates.

Sporadic groups (Mathematics) --- Finite simple groups --- Finite simple groups. --- Symmetry groups. --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Representations of groups --- Simple groups, Finite --- Finite groups --- Linear algebraic groups --- Groups, Sporadic (Mathematics)

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Algebraic topology --- 51 <082.1> --- Mathematics--Series --- Classifying spaces. --- Localization theory. --- Finite simple groups. --- Espaces classifiants --- Localisation, Théorie de la --- Groupes simples finis --- Classifying spaces --- Finite simple groups --- Localization theory --- Categories (Mathematics) --- Homotopy theory --- Nilpotent groups --- Simple groups, Finite --- Finite groups --- Linear algebraic groups --- Spaces, Classifying --- Fiber bundles (Mathematics) --- Fiber spaces (Mathematics) --- Espaces classifiants. --- Localisation, Théorie de la.