Memoirs of the American Mathematical Society 2013; 150 pp; softcover Volume: 226 ISBN10: 082188803X ISBN13: 9780821888032 List Price: US$83 Individual Members: US$49.80 Institutional Members: US$66.40 Order Code: MEMO/226/1061
 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 counterexample 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
