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Group theory --- Physics --- Representations of groups. --- Symmetry groups. --- Représentations de groupes --- Groupes symétriques --- Representations of groups --- Représentations de groupes --- Groupes symétriques --- Symmetry groups --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Group representation (Mathematics) --- Groups, Representation theory of

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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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Group theory --- Symmetry groups. --- Modules (Algebra) --- Operator theory. --- Groupes symétriques --- Modules (Algèbre) --- Théorie des opérateurs --- 51 <082.1> --- Mathematics--Series --- Groupes symétriques --- Modules (Algèbre) --- Théorie des opérateurs --- Operator theory --- Symmetry groups --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Representations of groups --- Functional analysis --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra)

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512.54 --- Symmetry groups --- -Point defects --- -Crystallography, Mathematical --- #WSCH:AAS1 --- Crystallography --- Crystallometry --- Mathematical crystallography --- Crystals --- Lattice theory --- Defects, Point --- Dislocations in crystals --- Impurity centers --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Representations of groups --- Groups. Group theory --- Tables --- Mathematics --- Mathematical models --- Defects --- Crystallography, Mathematical. --- Point defects --- Tables. --- 512.54 Groups. Group theory

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Group theory --- fysicochemie --- Mathematical physics --- Chemical and physical cristallography --- Representations of groups. --- Symmetry groups. --- Groups, Symmetry --- Symmetric groups --- Crystallography, Mathematical --- Quantum theory --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory. --- Mathematical physics. --- Physique mathématique. --- Physical mathematics --- Physics --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Mathematics --- 512.54 --- 512.54 Groups. Group theory --- Groups. Group theory --- Chemical and physical crystallography