New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
Rank 3 Amalgams
Bernd Stellmacher, University of Bielefeld, Germany, and Franz Georg Timmesfeld, University of Giessen, Germany
 SEARCH THIS BOOK:
Memoirs of the American Mathematical Society
1998; 123 pp; softcover
Volume: 136
ISBN-10: 0-8218-0870-2
ISBN-13: 978-0-8218-0870-2
List Price: US$50 Individual Members: US$30
Institutional Members: US\$40
Order Code: MEMO/136/649

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.

Graduate students and research mathematicians working in classical linear algebraic groups.

• Weak $$(B,N,)$$-pairs of Rank 2
• The Graph $$\Gamma$$
• The structure of $$\overline L_\delta$$ and $$\overline Z_\delta$$
• The case $$b\geq 2$$
• The case $$b=0$$
• The case $$b=1$$ and the proof of Theorems 1 and 4