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The main result describes completely the maximal factorizations of all the finite simple groups and their automorphism groups. As a consequence, a classification of the maximal subgroups of the finite alternating and symmetric groups is obtained.
The structure space S(M) of a closed topological m-manifold M classifies bundles whose fibers are closed m-manifolds equipped with a homotopy equivalence to M. We construct a highly connected map from S(M) to a concoction of algebraic L-theory and algebraic K-theory spaces assoc…