Theory of finite simple groups /

Theory of finite simple groups /

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Bibliographic Details
Author / Creator:Michler, G. (Gerhard), 1938-
Imprint:Cambridge : Cambridge University Press, 2006.
Description:ix, 662 p. : ill. ; 24 cm. + 1 DVD-ROM (4 3/4 in.)
Language:English
Series:New mathematical monographs ; 8
Subject:
Finite simple groups.
Finite simple groups.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6203706
Hidden Bibliographic Details
ISBN:0521866251 (hbk.)
9780521866255 (hbk.)
Notes:Includes bibliographical references and index.
Standard no.:9780521866255
Table of Contents:
  • Acknowledgements
  • List of symbols
  • Introduction
  • 1. Prerequisites from group theory
  • 1.1. Presentations of groups
  • 1.2. Generalized quaternion groups
  • 1.3. 2-Groups without non-cyclic abelian characteristic subgroups
  • 1.4. Transfer and fusion of elements
  • 1.5. Coprime group actions
  • 1.6. Simple groups with dihedral or semi-dihedral Sylow 2-subgroups
  • 1.7. Simple groups with strongly embedded subgroups
  • 2. Group representations and character theory
  • 2.1. Algebras, modules and representations
  • 2.2. Conjugacy classes of finite groups
  • 2.3. Characters of finite groups
  • 2.4. Characters and algebraic integers
  • 2.5. Tensor products
  • 2.6. Induction and restriction
  • 2.7. Frobenius groups and exceptional characters
  • 2.8. Brauer's characterization of characters
  • 2.9. Projective representations and central extensions
  • 3. Modular representation theory
  • 3.1. Existence of splitting p-modular systems
  • 3.2. Indecomposable modules
  • 3.3. Semi-perfect rings
  • 3.4. Group lattices and Heller modules
  • 3.5. Relative-projective modules and homomorphisms
  • 3.6. Blocks of finite groups
  • 3.7. Defect groups
  • 3.8. Brauer's first main theorem
  • 3.9. Support and kernel of a block idempotent
  • 3.10. Vertices and sources
  • 3.11. Modular characters of finite groups
  • 3.12. Blocks of defect zero
  • 3.13. Green correspondence
  • 3.14. Blocks and normal subgroups
  • 3.15. Blocks with normal defect groups
  • 3.16. Brauer's second and third main theorems
  • 3.17. Blocks of defect one
  • 4. Group order formulas and structure theorem
  • 4.1. Suzuki's group order formula
  • 4.2. Thompson's group order formula
  • 4.3. Groups with a unique conjugacy class of involutions
  • 4.4. Brauer's group order formula
  • 4.5. A theorem of G. Frobenius
  • 4.6. Brauer-Suzuki Theorem
  • 4.7. Glauberman's Z*-Theorem
  • 4.8. Structure theorem
  • 5. Permutation representations
  • 5.1. Permutation groups
  • 5.2. Orbits, stabilizers and group order
  • 5.3. Conjugacy classes of permutation groups
  • 5.4. Endomorphism rings of permutation modules
  • 5.5. Intersection algebras
  • 5.6. Character formula of Michler and Weller
  • 5.7. Algorithm for computing character values
  • 5.8. Completion of concrete character table calculations
  • 6. Concrete character tables of matrix groups
  • 6.1. Norton's irreducibility criterion
  • 6.2. From matrix groups to permutation groups
  • 6.3. Conjugacy classes of matrix groups
  • 6.4. Example of a concrete character table calculation
  • 7. Methods for constructing finite simple groups
  • 7.1. Free products with an amalgamated subgroup
  • 7.2. Irreducible representations of free products with amalgamated subgroups
  • 7.3. Kratzer's algorithm computing compatible characters
  • 7.4. Michler's algorithm constructing simple groups from given centralizers
  • 7.5. Uniqueness criterion
  • 8. Finite simple groups with proper satellites
  • 8.1. Mathieu groups M[subscript 11] and M[subscript 12]
  • 8.2. Mathieu groups M[subscript 22], M[subscript 23] and M[subscript 24]
  • 8.3. The satellites of M[subscript 24]
  • 8.4. Generating matrices of the Held group He in GL[subscript 51](11)
  • 8.5. Janko's sporadic groups J[subscript 2] and J[subscript 3]
  • 8.6. Simple satellites of the alternating groups
  • 9. Janko group J[subscript 1]
  • 9.1. Structure of the given centralizer
  • 9.2. Character table of groups of J[subscript 1]-type
  • 9.3. Existence Proof
  • 9.4. Uniqueness Proof
  • 10. Higman-Sims group HS
  • 10.1. Structure of the given centralizer
  • 10.2. Fusion
  • 10.3. Existence proof of HS inside GL[subscript 22](11)
  • 10.4. Uniqueness of HS
  • 10.5. A Presentation for Aut(HS)
  • 10.6. Representatives of conjugacy classes
  • 10.7. Character tables
  • 11. Harada group Ha
  • 11.1. The centralizer of a 2-central involution
  • 11.2. The existence proof
  • 11.3. Uniqueness
  • 11.4. Representatives of conjugacy classes
  • 11.5. Character tables
  • 11.6. Generating matrices A,B,C [isin] GL[subscript 133](19) of G
  • 12. Thompson group Th
  • 12.1. The centralizer of a 2-central involution
  • 12.2. Conjugacy classes of elements of even order
  • 12.3. Existence proof of Th inside GL[subscript 248](11)
  • 12.4. Determination of the 3-singular conjugacy classes
  • 12.5. The 5-, 7- and 13-singular conjugacy classes
  • 12.6. Group order
  • 12.7. Uniqueness proof and concrete character table
  • 12.8. Representatives of conjugacy classes
  • 12.9. Character tables
  • 12.10. Partial character table of matrix group 25
  • References
  • Index

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