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Rank 3 Amalgams
Bernd Stellmacher, University of Bielefeld, Germany, and Franz Georg Timmesfeld, University of Giessen, Germany
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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$47
Individual Members: US$28.20
Institutional Members: US$37.60
Order Code: MEMO/136/649
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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) \(G = \langle P_i|i \in I\rangle\),

(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

  • Introduction
  • Weak \((B,N,)\)-pairs of Rank 2
  • Modules
  • 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
  • The proof of Theorems 2 and 3
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