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...

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Bibliographic Details

Main Author:	Curtis, Robert 1946- (Author)
Format:	Electronic eBook
Language:	English
Published:	Cambridge Cambridge University Press 2007
Series:	Encyclopedia of mathematics and its applications volume 111
Subjects:	Sporadic groups (Mathematics) Finite simple groups Symmetry groups Symmetrische Gruppe Sporadische Gruppe
Online Access:	BSB01 FHN01 Volltext
Summary:	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
Item Description:	Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Physical Description:	1 online resource (xiv, 317 pages)
ISBN:	9780511661792
DOI:	10.1017/CBO9780511661792