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Acknowledgements xi
List of symbols xii
Introduction 1
Prerequisites from group theory 8
Presentations of groups 9
Generalized quaternion groups 12
2-Groups without non-cyclic abelian characteristic subgroups 15
Transfer and fusion of elements 25
Coprime group actions 34
Simple groups with dihedral or semi-dihedral Sylow 2-subgroups 38
Simple groups with strongly embedded subgroups 40
Group representations and character theory 42
Algebras, modules and representations 43
Conjugacy classes of finite groups 52
Characters of finite groups 55
Characters and algebraic integers 64
Tensor products 68
Induction and restriction 74
Frobenius groups and exceptional characters 82
Brauer's characterization of characters 90
Projective representations and central extensions 97
Modular representation theory 110
Existence of splitting p-modular systems 112
Indecomposable modules 123
Semi-perfect rings 128
Group latticesand Heller modules 137
Relative-projective modules and homomorphisms 144
Blocks of finite groups 153
Defect groups 160
Brauer's first main theorem 163
Support and kernel of a block idempotent 170
Vertices and sources 174
Modular characters of finite groups 181
Blocks of defect zero 187
Green correspondence 189
Blocks and normal subgroups 200
Blocks with normal defect groups 206
Brauer's second and third main theorems 212
Blocks of defect one 222
Group order formulas and structure theorem 242
Suzuki's group order formula 243
Thompson's group order formula 246
Groups with a unique conjugacy class of involutions 248
Brauer's group order formula 256
A theorem of G. Frobenius 259
Brauer-Suzuki Theorem 260
Glauberman's Z*-Theorem 266
Structure theorem 269
Permutation representations 277
Permutation groups 278
Orbits, stabilizers and group order 281
Conjugacy classes of permutation groups 289
Endomorphism rings of permutation modules 295
Intersection algebras 301
Character formula of Michler and Weller 307
Algorithm for computing character values 314
Completion of concrete character table calculations 316
Concrete character tables of matrix groups 320
Norton's irreducibility criterion 320
From matrix groups to permutation groups 324
Conjugacy classes of matrix groups 326
Example of a concrete character table calculation 328
Methods for constructing finite simple groups 333
Free products with an amalgamated subgroup 334
Irreducible representations of free products with amalgamated subgroups 341
Kratzer's algorithm computing compatible characters 348
Michler's algorithm constructing simple groups from given centralizers 354
Uniqueness criterion 364
Finite simple groups with proper satellites 376
Mathieu groups M[subscript 11] and M[subscript 12] 377
Mathieu groups M[subscript 22], M[subscript 23] and M[subscript 24] 388
The satellites of M[subscript 24] 397
Generating matrices of the Held group He in GL[subscript 51](11) 406
Janko's sporadic groups J[subscript 2] and J[subscript 3] 409
Simple satellites of the alternating groups 418
Janko group J[subscript 1] 433
Structure of the given centralizer 433
Character table of groups of J[subscript 1]-type 435
Existence Proof 447
Uniqueness Proof 452
Higman-Sims group HS 455
Structure of the given centralizer 455
Fusion 457
Existence proof of HS inside GL[subscript 22](11) 473
Uniqueness of HS 476
A Presentation for Aut(HS) 478
Representatives of conjugacy classes 480
Character tables 483
Harada group Ha 487
The centralizer of a 2-central involution 487
The existence proof 491
Uniqueness 497
Representatives of conjugacy classes 525
Character tables 530
Generating matrices A,B,C [isin] GL[subscript 133](19) of G 546
Thompson group Th 554
The centralizer of a 2-central involution 555
Conjugacy classes of elements of even order 557
Existence proof of Th inside GL[subscript 248](11) 561
Determination of the 3-singular conjugacy classes 571
The 5-, 7- and 13-singular conjugacy classes 598
Group order 607
Uniqueness proof and concrete character table 611
Representatives of conjugacy classes 616
Character tables 622
Partial character table of matrix group 25 641
References 645
Index 656
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Add Theory and Finite Simple Groups (New Mathematical Monographs Series #8), This book provides the first representation theoretic and algorithmic approach to the theory of abstract finite simple groups. It presents self-contained proofs of classical and new group order formulas, and a new structure theorem for abstract finite sim, Theory and Finite Simple Groups (New Mathematical Monographs Series #8) to the inventory that you are selling on WonderClubX
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Add Theory and Finite Simple Groups (New Mathematical Monographs Series #8), This book provides the first representation theoretic and algorithmic approach to the theory of abstract finite simple groups. It presents self-contained proofs of classical and new group order formulas, and a new structure theorem for abstract finite sim, Theory and Finite Simple Groups (New Mathematical Monographs Series #8) to your collection on WonderClub |