The Local Structure for Finite Groups with a Large $p$-Subgroup (Memoirs of the American Mathematical Society)

Meierfrankenfeld, U./ Stellmacher, B./ Stroth, G.

American Mathematical Society（2016/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 342 p.
• 言語 ENG
• 商品コード 9781470418779
• DDC分類 512.23

Full Description

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 $L$.

Contents

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