Symmetric generation of groups : with applications to many of the sporadic finite simple groups
著者
書誌事項
Symmetric generation of groups : with applications to many of the sporadic finite simple groups
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 111）
Cambridge University Press, 2007
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注記
Includes bibliographical references (p. 309-314) and index
内容説明・目次
内容説明
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.
目次
- Preface
- Acknowledgements
- Part I. Motivation: 1. The Mathieu group M12
- 2. The Mathieu group M24
- Part II. Involutory Symmetric Generators: 3. The progenitor
- 4. Classical examples
- 5. Sporadic simple groups
- Part III. Non-involutory Symmetric Generators: 6. The progenitor
- 7. Images of these progenitors.
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