
eBook ISBN: | 978-1-4704-2948-5 |
Product Code: | MEMO/242/1147.E |
List Price: | $108.00 |
MAA Member Price: | $97.20 |
AMS Member Price: | $64.80 |

eBook ISBN: | 978-1-4704-2948-5 |
Product Code: | MEMO/242/1147.E |
List Price: | $108.00 |
MAA Member Price: | $97.20 |
AMS Member Price: | $64.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 242; 2016; 342 ppMSC: Primary 20
Let \(p\) be a prime, \(G\) a finite \(\mathcal{K}_p\)-group \(S\) a Sylow \(p\)-subgroup of \(G\) and \(Q\) a large subgroup of \(G\) in \(S\) (i.e., \(C_G(Q) \leq Q\) and \(N_G(U) \leq N_G(Q)\) for \(1 \ne U \leq C_G(Q)\)). Let \(L\) be any subgroup of \(G\) with \(S\leq L\), \(O_p(L)\neq 1\) and \(Q\ntrianglelefteq L\). In this paper the authors determine the action of \(L\) on the largest elementary abelian normal \(p\)-reduced \(p\)-subgroup \(Y_L\) of \(L\).
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Table of Contents
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Chapters
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Introduction
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1. Definitions and Preliminary Results
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2. The Case Subdivision and Preliminary Results
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3. The Orthogonal Groups
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4. The Symmetric Case
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5. The Short Asymmetric Case
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6. The Tall $char\, p$-Short Asymmetric Case
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7. The $char\, p$-Tall $Q$-Short Asymmetric Case
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8. The $Q$-Tall Asymmetric Case I
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9. The $Q$-tall Asymmetric Case II
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10. Proof of the Local Structure Theorem
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A. Module theoretic Definitions and Results
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B. Classical Spaces and Classical Groups
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C. FF-Module Theorems and Related Results
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D. The Fitting Submodule
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E. The Amalgam Method
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Bibliography
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Additional Material
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Let \(p\) be a prime, \(G\) a finite \(\mathcal{K}_p\)-group \(S\) a Sylow \(p\)-subgroup of \(G\) and \(Q\) a large subgroup of \(G\) in \(S\) (i.e., \(C_G(Q) \leq Q\) and \(N_G(U) \leq N_G(Q)\) for \(1 \ne U \leq C_G(Q)\)). Let \(L\) be any subgroup of \(G\) with \(S\leq L\), \(O_p(L)\neq 1\) and \(Q\ntrianglelefteq L\). In this paper the authors determine the action of \(L\) on the largest elementary abelian normal \(p\)-reduced \(p\)-subgroup \(Y_L\) of \(L\).
-
Chapters
-
Introduction
-
1. Definitions and Preliminary Results
-
2. The Case Subdivision and Preliminary Results
-
3. The Orthogonal Groups
-
4. The Symmetric Case
-
5. The Short Asymmetric Case
-
6. The Tall $char\, p$-Short Asymmetric Case
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7. The $char\, p$-Tall $Q$-Short Asymmetric Case
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8. The $Q$-Tall Asymmetric Case I
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9. The $Q$-tall Asymmetric Case II
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10. Proof of the Local Structure Theorem
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A. Module theoretic Definitions and Results
-
B. Classical Spaces and Classical Groups
-
C. FF-Module Theorems and Related Results
-
D. The Fitting Submodule
-
E. The Amalgam Method
-
Bibliography