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# The Classification of Quasithin Groups: II. Main Theorems: The Classification of Simple QTKE-groups

### About this Title

**Michael Aschbacher**, *California Institute of Technology, Pasadena, CA* and **Stephen D. Smith**, *University of Illinois at Chicago, Chicago, IL*

Publication: Mathematical Surveys and Monographs

Publication Year:
2004; Volume 112

ISBNs: 978-0-8218-3411-4 (print); 978-1-4704-1339-2 (online)

DOI: https://doi.org/10.1090/surv/112

MathSciNet review: MR2097624

MSC: Primary 20D05; Secondary 20C20

### Table of Contents

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**Front/Back Matter**

**Part 1. Structure of QTKE-groups and the main case division **

- 1. Structure and intersection properties of 2-locals
- 2. Classifying the groups with $|\mathcal {M}(T)|= 1$
- 3. Determining the cases for $L \in \mathcal {L}^*_f(G,T)$
- 4. Pushing up in QTKE-groups

**Part 2. The treatment of the generic case **

- 5. The generic case: $L_2(2^n)$ in $\mathcal {L}_f$ and $n(H) > 1$
- 6. Reducing $\textbf {L_2(2^n)}$ to $\textbf {n = 2}$ and V orthogonal

**Part 3. Modules which are not FF-modules **

- 7. Eliminating cases corresponding to no shadow
- 8. Eliminating shadows and characterizing the $\textbf {J_4}$ example
- 9. Eliminating $\Omega ^+_4(2^n)$ on its orthogonal module

**Part 4. Pairs in the FSU over $\textbf {F}_{2^n}$ for $n > 1$. **

- 10. The case $L \in \mathcal {L}^*_f(G,T)$ not normal in $M$
- 11. Elimination of $\textbf {L_3(2^n)}$, $\textbf {Sp_4(2^n)}$, and $\textbf {G_2(2^n)}$ for $\textbf {n > 1}$

**Part 5. Groups over $\textbf {F}_2$ **

- 12. Larger groups over $\textbf {F_2}$ in $\mathcal {L}^*_f(G,T)$
- 13. Mid-size groups over $\textbf {F_2}$
- 14. $\textbf {L_3(2)}$ in the FSU, and $\textbf {L_2(2)}$ when $\textbf {\mathcal {L}_f(G,T)}$ is empty

**Part 6. The case $\mathcal {L}_f(G,T)$ empty **

**Part 7. The Even Type Theorem **