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1 | Introduction | 1 |
1.1 | Symplectic Amalgams | 2 |
1.2 | Goldchmidt G[subscript 4]-amalgam Again | 19 |
2 | Preliminaries | 21 |
2.1 | Some Group Theory Results | 22 |
2.2 | Some Representation Theory Results | 29 |
2.3 | Sesquilinear Forms | 35 |
2.4 | Two Theorems of McLaughlin | 40 |
2.5 | Ultraspecial and Extraspecial Groups | 42 |
2.6 | Tensor Products and Group Actions on p-Groups | 45 |
2.7 | The Goldschmidt Amalgams | 48 |
3 | The Structure of SL[subscript 2](q) and its Modules | 53 |
3.1 | Group Theoretic Properties of SL[subscript 2](q) | 53 |
3.2 | Modules for SL[subscript 2](q) | 56 |
4 | Elementary Properties of Symplectic Amalgams | 67 |
4.1 | The Coset Graph | 67 |
4.2 | Proof of Theorem 1.6 | 69 |
5 | The Structure of Q[subscript [alpha]] | 81 |
6 | The L[subscript [beta]]-Chief Factors in V[subscript [beta]] | 93 |
7 | Reduced Symplectic Amalgams | 113 |
7.1 | A Reduced Symplectic Subamalgam | 113 |
7.2 | Reduced Amalgams and Consequences of Theorem 6.1 | 118 |
8 | The Largest Normal p'-Subgroup of L[subscript [beta]]/Q[subscript [beta]] | 125 |
9 | The Components of L[subscript [beta]]/Q[subscript [beta]] | 141 |
9.1 | The Action of L[subscript [beta]] on Comp[subscript p](L[subscript [beta]]) | 142 |
9.2 | Two or more Normal Components in L[subscript [beta]]/Q[subscript [beta]] | 148 |
10 | The Reduction to Quasisimple when C[subscript U[alpha]](U[subscript [alpha]]/Z[subscript [alpha]]) [neither less than, nor equal to] Q[subscript [beta]] | 163 |
11 | A First Look at the Amalgams with |V[subscript [beta]]/Z(V[subscript [beta]])| = q[superscript 4] | 177 |
11.1 | A Characteristic 3 Amalgam | 178 |
11.2 | The Proof of Theorem 11.1 | 180 |
12 | The Story so Far | 187 |
13 | Groups of Lie Type | 189 |
13.1 | Weyl Groups and Parabolic Subgroups | 193 |
13.2 | Sylow p-subgroups of Lie Type Groups | 195 |
13.3 | Automorphisms and Centres | 197 |
13.4 | The Order of Abelian p-subgroups | 199 |
13.5 | Extremal Subgroups | 202 |
14 | Modules for Groups of Lie Type | 215 |
14.1 | Modules in Characteristic p | 215 |
14.2 | Module Results for Low Rank Groups of Lie Type | 220 |
14.3 | Modules for Lie Type Groups and (2,q)-Transvections | 224 |
14.4 | Natural Modules for Orthogonal Groups | 231 |
14.5 | Natural Modules for the Symplectic Groups | 234 |
14.6 | Natural Modules for G[subscript 2](q) | 237 |
14.7 | Some Spin Modules | 239 |
14.8 | Modules for Lie Type Groups in Non-defining Characteristic | 240 |
14.9 | Some Non-containments | 247 |
15 | Sporadic Simple Groups and Their Modules | 249 |
16 | Alternating Groups and Their Modules | 257 |
17 | Rank One Groups | 265 |
18 | Lie Type Groups in Characteristic p and Rank [greater than or equal to] 2 | 271 |
18.1 | A Subamalgam of A | 272 |
18.2 | The Examples | 285 |
18.3 | L[subscript [beta]]/Q[subscript [beta]] a Symplectic Group and V[subscript [beta]]/Z(V[subscript [beta]]) a Spin Module | 290 |
19 | Lie Type Groups and Natural Modules | 293 |
19.1 | The Symplectic and Orthogonal Groups | 295 |
19.2 | Sp[subscript 4](2) - A Special Case | 305 |
19.3 | Groups of Type G[subscript 2](q) | 310 |
20 | Lie Type Groups in Characteristic not p | 313 |
21 | Alternating Groups | 315 |
21.1 | Large Alternating Groups | 315 |
21.2 | Small Alternating Groups | 319 |
22 | Sporadic Simple Groups | 325 |
23 | The Proof of the Main Theorems | 327 |
24 | A Brief Survey of Amalgam Results | 331 |
24.1 | Amalgam Results | 331 |
24.2 | Pushing-up | 340 |
References | 345 | |
Index | 357 |
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Add Symplectic Amalgams, The account is for the most part self-contained and the wealth of detail makes this book an excellent introduction to these recent developments for graduate students, as well as a valuable resource and reference for specialists in the area., Symplectic Amalgams to the inventory that you are selling on WonderClubX
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Add Symplectic Amalgams, The account is for the most part self-contained and the wealth of detail makes this book an excellent introduction to these recent developments for graduate students, as well as a valuable resource and reference for specialists in the area., Symplectic Amalgams to your collection on WonderClub |