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Isolated Involutions in Finite Groups
Rebecca Waldecker, Martin-Luther-Universität Halle-Wittenberg, Germany
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Memoirs of the American Mathematical Society
2013; 150 pp; softcover
Volume: 226
ISBN-10: 0-8218-8803-X
ISBN-13: 978-0-8218-8803-2
List Price: US$83
Individual Members: US$49.80
Institutional Members: US$66.40
Order Code: MEMO/226/1061
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This text provides a new proof of Glauberman's Z*-Theorem under the additional hypothesis that the simple groups involved in the centraliser of an isolated involution are known simple groups.

Table of Contents

  • Introduction
  • Preliminaries
  • Isolated involutions
  • A minimal counter-example to Glauberman's Z*-theorem
  • Balance and signalizer functors
  • Preparatory results for the local analysis
  • Maximal subgroups containing \(C\)
  • The \(2\)-rank of \(O_{2',2}(C)\)
  • Components of \(\overline{C}\) and the Soluble Z*-theorem
  • Unbalanced components
  • The \(2\)-rank of \(G\)
  • The F*-structure theorem
  • More involutions
  • The endgame
  • The final contradiction and the Z*-theorem for \(\mathcal{K}_2\)-Groups
  • Bibliography
  • Index
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