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We investigate a stronger formulation of Webb's conjecture on thecontractibilty of the orbit space of the p-subgroup complexes in terms offinite topological spaces. The original conjecture, which was first proved bySymonds and, more recently, by Bux, Libman and Linckelmann, can be restated interms of the topology of certain finite spaces. We propose a strongerconjecture, and prove various particular cases by combining fusion theory offinite groups and homotopy theory of finite spaces.

A stronger reformulation of Webb's conjecture in terms of finite topological spaces