The Local Structure for Finite Groups With a Large $p$-Subgroup

ISBN-13: 9781470418779 / Angielski

U. Meierfrankenfeld;B. Stellmacher;G. Stroth

Opis

Let $p$ be a prime, $G$ a finite $mathcal_p$-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 $1 e U leq C_G(Q)$). Let $L$ be any subgroup of $G$ with $Sleq L$, $O_p(L)eq 1$ and $Qtrianglelefteq L$. In this paper the authors determine the action of $L$ on the largest elementary abelian normal $p$-reduced $p$-subgroup $Y_L$ of $L$.

Spis treści

• Introduction
• Chapter 1. Definitions and Preliminary Results
• Chapter 2. The Case Subdivision and Preliminary Results
• Chapter 3. The Orthogonal Groups
• Chapter 4. The Symmetric Case
• Chapter 5. The Short Asymmetric Case
• Chapter 6. The Tall charpcharp-Short Asymmetric Case
• Chapter 7. The charpcharp-Tall QQ-Short Asymmetric Case
• Chapter 8. The QQ-Tall Asymmetric Case I
• Chapter 9. The QQ-tall Asymmetric Case II
• Chapter 10. Proof of the Local Structure Theorem
• Appendix A. Module theoretic Definitions and Results
• Appendix B. Classical Spaces and Classical Groups
• Appendix C. FF-Module Theorems and Related Results
• Appendix D. The Fitting Submodule
• Appendix E. The Amalgam Method
• Bibliography