Memoirs of the American Mathematical Society 2006; 102 pp; softcover Volume: 180 ISBN10: 0821838288 ISBN13: 9780821838280 List Price: US$65 Individual Members: US$39 Institutional Members: US$52 Order Code: MEMO/180/848
 We prove here the MartinoPriddy conjecture at the prime \(2\): the \(2\)completions of the classifying spaces of two finite groups \(G\) and \(G'\) are homotopy equivalent if and only if there is an isomorphism between their Sylow \(2\)subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group \(G\), the second higher derived functor of the inverse limit vanishes for a certain functor \(\mathcal{Z}_G\) on the \(2\)subgroup orbit category of \(G\). The proof of this result uses the classification theorem for finite simple groups. Table of Contents  Introduction
 Higher limits over orbit categories
 Reduction to simple groups
 A relative version of \(\Lambda\)functors
 Subgroups which contribute to higher limits
 Alternating groups
 Groups of Lie type in characteristic two
 Classical groups of Lie type in odd characteristic
 Exceptional groups of Lie type in odd characteristic
 Sproadic groups
 Computations of \(\mathrm{lim}^1(\mathcal{Z}_G)\)
 Bibliography
