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Quaternion Fusion Packets [Minkštas viršelis]

  • Formatas: Paperback / softback, 456 pages, aukštis x plotis: 254x178 mm, weight: 794 g
  • Serija: Contemporary Mathematics
  • Išleidimo metai: 30-May-2021
  • Leidėjas: American Mathematical Society
  • ISBN-10: 1470456656
  • ISBN-13: 9781470456658
Kitos knygos pagal šią temą:
Quaternion Fusion PacketsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 456 pages, aukštis x plotis: 254x178 mm, weight: 794 g
  • Serija: Contemporary Mathematics
  • Išleidimo metai: 30-May-2021
  • Leidėjas: American Mathematical Society
  • ISBN-10: 1470456656
  • ISBN-13: 9781470456658
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781470456658.html
Raktažodžiai:
Let $p$ be a prime and$S$ a finite $p$-group. A $p$-fusion system on $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory. The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
Background and overview 1(2)
Chapter 0 Introduction 3(4)
Chapter 1 The major theorems and some background 7(14)
1.1 Theorems 1 through 8
7(3)
1.2 Background
10(3)
1.3 An outline of the proof
13(6)
Basics and examples
19(2)
Chapter 2 Some basic results 21(32)
2.1 Preliminary lemmas
21(6)
2.2 Solvable components
27(7)
2.3 Intrinsic SL2[ m]-components
34(5)
2.4 A sufficient condition for quaternion fusion packets
39(1)
2.5 Basic results on fusion packets
39(2)
2.6 The case z belongs to Z(F)
41(4)
2.7 F = SOτ
45(3)
2.8 Modules for groups with a strongly embedded subgroup
48(5)
Chapter 3 Results on τ 53(26)
3.1 δ(τ), η(τ), and μ(τ)
54(10)
3.2 The graph A
64(2)
3.3 More basic lemmas
66(6)
3.4 Generating F
72(7)
Chapter 4 W(τ) and M(τ) 79(16)
4.1 3-transposition groups
79(7)
4.2 The groups in M(τ)
86(4)
4.3 The groups ω(Φ,m)
90(5)
Chapter 5 Some examples 95(42)
5.1 AEn
96(6)
5.2 The 2-share of the order of some groups
102(3)
5.3 Orthogonal groups and packets
105(4)
5.4 Linear, unitary, and symplectic groups and packets
109(4)
5.5 Exceptional groups and packets
113(4)
5.6 Fs(G) is simple
117(3)
5.7 Lπd[ m] and ω(Ad-1,m)
120(3)
5.8 ω(Dn,m)
123(4)
5.9 ω(Cn,m) and 2ω(Cn,m)
127(1)
5.10 Some constrained examples
128(4)
5.11 Summary of basics
132(3)
Theorems 2 through 5
135(2)
Chapter 6 Theorems 2 and 4 137(36)
6.1 D(τ)c
137(3)
6.2 Beginning the case z belongs to O2(F)
140(6)
6.3 The case e not < or = to NG(K)
146(13)
6.4 Subnormal closure
159(3)
6.5 F*(F)
162(4)
6.6 z not in O2(T)
166(4)
6.7 The proof of Theorem 2
170(3)
Chapter 7 Theorems 3 and 5 173(22)
7.1 Packets of width 1
173(11)
7.2 A(z) not = to 0
184(9)
Coconnectedness
193(2)
Chapter 8 τ° not coconnected 195(10)
8.1 Dc disconnected
195(8)
Theorem 6
203(2)
Chapter 9 Ω = Ω(z) of order 2 205(50)
9.1 |Ω(z)| = 2
205(6)
9.2 Generation when |Ω(z)| = 2
211(4)
9.3 |Ω(z)| = 2 and Z union O(z) {z}
215(8)
9.4 |Ω(z)| = 2 and D*(z) = D(z)
223(17)
9.5 |Ω(z)| = 2 and μ isomorphic to S4
240(15)
Chapter 10 |Ω(z)| > 2 255(14)
10.1 |Ω(z)| = 4 and μ isomorphic to Weyl(D4)
255(8)
10.2 |Ω(z)| large
263(6)
Chapter 11 Some results on generation 269(36)
11.1 |Ω(z)| = 2, μ isomorphic to Weyl(Dn), n > or = to 4
269(4)
11.2 Generation
273(16)
11.3 More generation
289(3)
11.4 Essentials and normal subsystems
292(3)
11.5 Generating Ωbelongstod[ m]
295(5)
11.6 Generating AEk
300(5)
Chapter 12 |Ω(z)| = 2 and the proof of Theorem 6 305(36)
12.1 |Ω(z)| = 2, μ isomorphic to Weyl(D4)
305(7)
12.2 More |Ω(z)| = 2
312(13)
12.3 Completing |Ω(z)| = 2
325(13)
12.4 The proof of Theorem 6
338(1)
Theorems 7 and 8
339(2)
Chapter 13 |&Omgea;(z)| = 1 and µ abelian 341(34)
13.1 Systems with µ abelian
341(10)
13.2 Generic systems with µ abelian
351(9)
13.3 Symplectic groups and systems
360(2)
13.4 Linear and unitary groups and systems
362(4)
13.5 Generating symplectic and linear systems
366(5)
13.6 Finishing µ abelian
371(4)
Chapter 14 More generation 375(10)
14.1 A generation lemma
375(4)
14.2 A generation lemma for E8
379(6)
Chapter 15 |Ω(z)| = 1 and µ, nonabelian 385(48)
15.1 |Ω(z)| = 1
385(4)
15.2 The case r > 1
389(10)
15.3 Φ = Dn
399(4)
15.4 Φ = D4
403(7)
15.5 Φ = En
410(9)
15.6 Generating linear systems
419(3)
15.7 Wrapping up Φ = An
422(2)
15.8 Φ = En
424(7)
Theorem 1 and the Main Theorem
431(2)
Chapter 16 Proofs of four theorems 433(6)
16.1 The proof of Theorem 1
433(2)
16.2 Proofs of the Main Theorem and Theorems 6, 7, and 8
435(1)
16.3 Lie fusion packets
436(3)
References and Index 439(2)
Bibliography 441(2)
Index 443
Michael Aschbacher, California Institute of Technology, Pasadena, CA