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  1. Home
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  3. Symmetric Generation of Groups
  • Cited by 9
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
2007
Online ISBN:
9780511661792
DOI:
https://doi.org/10.1017/CBO9780511661792
Subjects:
Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
Series:
Encyclopedia of Mathematics and its Applications (111)
Information

Book description

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.

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