Symmetric Generation of Groups With Applications to Many of the Sporadic Finite Simple Groups

Name: Symmetric Generation of Groups With Applications to Many of the Sporadic Finite Simple Groups
Price: 130.86 USD
Availability: InStock
ISBN: 9780521857215

ISBN-10: 052185721X

ISBN-13: 9780521857215

Edition: 2007

Authors: Robert T. Curtis

List price: $199.99

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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…

Book details

List price: $199.99
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 7/5/2007
Binding: Hardcover
Pages: 332
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.562
Language: English

Robert T. Curtis is Professor of Combinatorial Algebra and Head of Pure Mathematics in the School of Mathematics at the University of Birmingham. He also holds the post of Librarian for the London Mathematical Society.



Preface


Acknowledgements



Motivation


Introduction to Part I



The Mathieu group M[subscript 12]



The combinatorial approach



The regular dodecahedron



The algebraic approach



Independent proofs



The Mathieu group M[subscript 24]



The combinatorial approach



The Klein map



The algebraic approach



Independent proofs


Conclusions to Part I



Involutory Symmetric Generators



The (involutory) progenitor



Free products of cyclic groups of order 2



Semi-direct products and the progenitor P



The Cayley graph of P over N



The regular graph preserved by P



Homomorphic images of P



The lemma



Further properties of the progenitor



Coxeter diagrams and Y-diagrams



Introduction to Magma and GAP



Algorithm for double coset enumeration



Systematic approach



Classical examples



The group PGL[subscript 2](7)



Exceptional behaviour of S[subscript n]



The 11-point biplane and PGL[subscript 2](11)



The group of the 28 bitangents



Sporadic simple groups



The Mathieu group M[subscript 22]



The Janko group J[subscript 1]



The Higman-Sims group



The Hall-Janko group and the Suzuki chain



The Mathieu groups M[subscript 12] and M[subscript 24]



The Janko group J[subscript 3]



The Mathieu group M[subscript 24] as control subgroup



The Fischer groups



Transitive extensions and the O'Nan group



Symmetric representation of groups



Appendix to Chapter 5



Non-Involutory Symmetric Generators



The (non-involutory) progenitor



Monomial automorphisms



Monomial representations



Monomial action of a control subgroup



Images of the progenitors in Chapter 6



The Mathieu group M[subscript 11]



The Mathieu group M[subscript 23]



The Mathieu group M[subscript 24]



Factoring out a 'classical' relator



The Suzuki chain and the Conway group



Systematic approach



Tabulated results



Some sporadic groups


References


Index