Symmetric generation of groups : with applications to many of the sporadic finite simple groups /
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| Author / Creator: | Curtis, Robert, 1946- |
|---|---|
| Imprint: | Cambridge : Cambridge University Press, 2007. |
| Description: | xiv, 317 p. : ill. (some col.) ; 24 cm. |
| Language: | English |
| Series: | Encyclopedia of mathematics and its applications ; 111 |
| Subject: | Sporadic groups (Mathematics) Finite simple groups. Symmetry groups. Finite simple groups. Sporadic groups (Mathematics) Symmetry groups. |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6493428 |
Table of Contents:
- Preface
- Acknowledgements
- I. Motivation
- Introduction to Part I
- 1. The Mathieu group M[subscript 12]
- 1.1. The combinatorial approach
- 1.2. The regular dodecahedron
- 1.3. The algebraic approach
- 1.4. Independent proofs
- 2. The Mathieu group M[subscript 24]
- 2.1. The combinatorial approach
- 2.2. The Klein map
- 2.3. The algebraic approach
- 2.4. Independent proofs
- Conclusions to Part I
- II. Involutory Symmetric Generators
- 3. The (involutory) progenitor
- 3.1. Free products of cyclic groups of order 2
- 3.2. Semi-direct products and the progenitor P
- 3.3. The Cayley graph of P over N
- 3.4. The regular graph preserved by P
- 3.5. Homomorphic images of P
- 3.6. The lemma
- 3.7. Further properties of the progenitor
- 3.8. Coxeter diagrams and Y-diagrams
- 3.9. Introduction to Magma and GAP
- 3.10. Algorithm for double coset enumeration
- 3.11. Systematic approach
- 4. Classical examples
- 4.1. The group PGL[subscript 2](7)
- 4.2. Exceptional behaviour of S[subscript n]
- 4.3. The 11-point biplane and PGL[subscript 2](11)
- 4.4. The group of the 28 bitangents
- 5. Sporadic simple groups
- 5.1. The Mathieu group M[subscript 22]
- 5.2. The Janko group J[subscript 1]
- 5.3. The Higman-Sims group
- 5.4. The Hall-Janko group and the Suzuki chain
- 5.5. The Mathieu groups M[subscript 12] and M[subscript 24]
- 5.6. The Janko group J[subscript 3]
- 5.7. The Mathieu group M[subscript 24] as control subgroup
- 5.8. The Fischer groups
- 5.9. Transitive extensions and the O'Nan group
- 5.10. Symmetric representation of groups
- 5.11. Appendix to Chapter 5
- III. Non-Involutory Symmetric Generators
- 6. The (non-involutory) progenitor
- 6.1. Monomial automorphisms
- 6.2. Monomial representations
- 6.3. Monomial action of a control subgroup
- 7. Images of the progenitors in Chapter 6
- 7.1. The Mathieu group M[subscript 11]
- 7.2. The Mathieu group M[subscript 23]
- 7.3. The Mathieu group M[subscript 24]
- 7.4. Factoring out a 'classical' relator
- 7.5. The Suzuki chain and the Conway group
- 7.6. Systematic approach
- 7.7. Tabulated results
- 7.8. Some sporadic groups
- References
- Index
