eBook ISBN:  9781470402389 
Product Code:  MEMO/136/649.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $30.00 
eBook ISBN:  9781470402389 
Product Code:  MEMO/136/649.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $30.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 136; 1998; 123 ppMSC: Primary 20
Let \(G\) be a group, \(p\) a fixed prime, \(I = {1,...,n}\) and let \(B\) and \(P_i, i \in I\) be a collection of finite subgroups of \(G\). Then \(G\) satisfies \(P_n\) (with respect to \(p\), \(B\) and \(P_i, i \in I\)) if:
(1) \(G = \langle P_ii \in I\rangle\),
(2) \(B\) is the normalizer of a \(pSylow\)subgroup in \(P_i\),
(3) No nontrivial normal subgroup of \(B\) is normal in \(G\),
(4) \(O^{p^\prime}(P_i/O_p(P_i))\) is a rank 1 Lietype group in char \(p\) (also including solvable cases).
If \(n = 2\), then the structure of \(P_1, P_2\) was determined by Delgado and Stellmacher. In this book the authors treat the case \(n = 3\). This has applications for locally finite, chamber transitive Titsgeometries and the classification of quasithin groups.
ReadershipGraduate students and research mathematicians working in classical linear algebraic groups.

Table of Contents

Chapters

0. Introduction

1. Weak ($B$, $N$)pairs of rank 2

2. Modules

3. The graph $\Gamma $

4. The structure of $\bar {L}_\delta $ and $\bar {Z}_\delta $

5. The case $b \geq 2$

6. The case $b = 0$

7. The case $b = 1$ and the proof of Theorems 1 and 4

8. The proof of Theorems 2 and 3


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Let \(G\) be a group, \(p\) a fixed prime, \(I = {1,...,n}\) and let \(B\) and \(P_i, i \in I\) be a collection of finite subgroups of \(G\). Then \(G\) satisfies \(P_n\) (with respect to \(p\), \(B\) and \(P_i, i \in I\)) if:
(1) \(G = \langle P_ii \in I\rangle\),
(2) \(B\) is the normalizer of a \(pSylow\)subgroup in \(P_i\),
(3) No nontrivial normal subgroup of \(B\) is normal in \(G\),
(4) \(O^{p^\prime}(P_i/O_p(P_i))\) is a rank 1 Lietype group in char \(p\) (also including solvable cases).
If \(n = 2\), then the structure of \(P_1, P_2\) was determined by Delgado and Stellmacher. In this book the authors treat the case \(n = 3\). This has applications for locally finite, chamber transitive Titsgeometries and the classification of quasithin groups.
Graduate students and research mathematicians working in classical linear algebraic groups.

Chapters

0. Introduction

1. Weak ($B$, $N$)pairs of rank 2

2. Modules

3. The graph $\Gamma $

4. The structure of $\bar {L}_\delta $ and $\bar {Z}_\delta $

5. The case $b \geq 2$

6. The case $b = 0$

7. The case $b = 1$ and the proof of Theorems 1 and 4

8. The proof of Theorems 2 and 3