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The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup
 
U. Meierfrankenfeld Michigan State University, East Lansing, MI
B. Stellmacher Christian-Albrechts-University of Kiel, Kiel, Germany
G. Stroth Martin-Luther-Unversität Halle-Wittenberg, Germany
The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup
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
The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup
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The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup
U. Meierfrankenfeld Michigan State University, East Lansing, MI
B. Stellmacher Christian-Albrechts-University of Kiel, Kiel, Germany
G. Stroth Martin-Luther-Unversität Halle-Wittenberg, Germany
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2422016; 342 pp
    MSC: 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. FF-Module Theorems and Related Results
    • D. The Fitting Submodule
    • E. The Amalgam Method
    • Bibliography
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2422016; 342 pp
MSC: 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 \(L\).

  • 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. FF-Module Theorems and Related Results
  • D. The Fitting Submodule
  • E. The Amalgam Method
  • Bibliography
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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