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Finite simple groups. --- Representations of groups. --- Groupes simples finis. --- Représentations de groupes. --- Groupes simples finis --- Représentations de groupes --- Finite groups --- Groups, Finite --- Group theory --- Modules (Algebra)

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Finite simple groups. --- Group theory. --- Groupes simples finis. --- Groupes, Théorie des. --- Lie groups.

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The finite simple groups are basic objects in algebra since many questions about general finite groups can be reduced to questions about the simple groups. Finite simple groups occur naturally in certain infinite families, but not so for all of them: the exceptions are called sporadic groups, a term used in the classic book of Burnside [Bur] to refer to the five Mathieu groups. There are twenty six sporadic groups, not definitively organized by any simple theme. The largest of these is the monster, the simple group of Fischer and Griess, and twenty of the sporadic groups are involved in the monster as subquotients. These twenty constitute the Happy Family, and they occur naturally in three generations. In this book, we treat the twelve sporadics in the first two generations. I like these twelve simple groups very much, so have chosen an exposition to appreciate their beauty, linger on details and develop unifying themes in their structure theory. Most of our book is accessible to someone with a basic graduate course in abstract algebra and a little experience with group theory, especially with permu­ tation groups and matrix groups. In fact, this book has been used as the basis for second-year graduate courses.

Group theory --- Finite simple groups. --- Groupes simples finis --- Group theory. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra

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Group theory --- Groupes, Théorie des --- Finite simple groups --- Groupes simples finis --- Groupes de lie --- Formulaire de mathematiques --- Representation des groupes de lie

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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