Equivalences of Classifying Spaces Completed at the Prime Two

Introduction; Higher limits over orbit categories; Reduction to simple groups; A relatice 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 $textrm{lim}1(mathcal{Z} G)$; Bibliography