Rank 3 Amalgams

Item Successfully Added to Cart

An error was encountered while trying to add the item to the cart. Please try again.

Continue Shopping

Go to Checkout

Please make all selections above before adding to cart

Share this page via the icons above, or by copying the link below:

Copy To Clipboard

Successfully Copied!

Rank 3 Amalgams

Bernd Stellmacher : University of Bielefeld, Bielefeld, Germany

Franz Georg Timmesfeld : University of Giessen, Giessen, Germany

eBook ISBN:	978-1-4704-0238-9
Product Code:	MEMO/136/649.E

List Price:	$50.00
MAA Member Price:	$45.00
AMS Member Price:	$30.00

Add to cart

Click above image for expanded view

Rank 3 Amalgams

Bernd Stellmacher : University of Bielefeld, Bielefeld, Germany

Franz Georg Timmesfeld : University of Giessen, Giessen, Germany

eBook ISBN:	978-1-4704-0238-9
Product Code:	MEMO/136/649.E

List Price:	$50.00
MAA Member Price:	$45.00
AMS Member Price:	$30.00

Add to cart

Book Details

Memoirs of the American Mathematical Society

Volume: 136; 1998; 123 pp

MSC: 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) $G = \langle P_i|i \in I\rangle$,
(2) $B$ is the normalizer of a $p-Sylow$-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 Lie-type 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 Tits-geometries and the classification of quasithin groups.

Readership

Graduate 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
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

Book Details
Table of Contents
Requests

Memoirs of the American Mathematical Society

Volume: 136; 1998; 123 pp

MSC: 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) $G = \langle P_i|i \in I\rangle$,

(2) $B$ is the normalizer of a $p-Sylow$-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 Lie-type 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 Tits-geometries and the classification of quasithin groups.

Readership

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

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

Please select which format for which you are requesting permissions.