eBook ISBN:  9781470429485 
Product Code:  MEMO/242/1147.E 
List Price:  $108.00 
MAA Member Price:  $97.20 
AMS Member Price:  $64.80 
eBook ISBN:  9781470429485 
Product Code:  MEMO/242/1147.E 
List Price:  $108.00 
MAA Member Price:  $97.20 
AMS Member Price:  $64.80 

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 \(L\).

Table of Contents

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

7. The $char\, p$Tall $Q$Short Asymmetric Case

8. The $Q$Tall Asymmetric Case I

9. The $Q$tall Asymmetric Case II

10. Proof of the Local Structure Theorem

A. Module theoretic Definitions and Results

B. Classical Spaces and Classical Groups

C. FFModule Theorems and Related Results

D. The Fitting Submodule

E. The Amalgam Method

Bibliography


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

7. The $char\, p$Tall $Q$Short Asymmetric Case

8. The $Q$Tall Asymmetric Case I

9. The $Q$tall Asymmetric Case II

10. Proof of the Local Structure Theorem

A. Module theoretic Definitions and Results

B. Classical Spaces and Classical Groups

C. FFModule Theorems and Related Results

D. The Fitting Submodule

E. The Amalgam Method

Bibliography