Symmetric Generation of Groups
(Book #111 in the Encyclopedia of Mathematics and its Applications Series)
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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.
Format:Hardcover
Language:English
ISBN:052185721X
ISBN13:9780521857215
Release Date:July 2007
Publisher:Cambridge University Press
Length:332 Pages
Weight:1.57 lbs.
Dimensions:0.8" x 6.6" x 9.3"
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