A p-local finite group is an algebraic structure which mimics the p-local structure in a finite group, and topologically corresponds to the p-completed classifying space. A central question in group theory is to what extend the local structure determines the global structure. In this talk I will present a homotopical approach to this question via p-local finite groups, and give some concrete local-to-global results for specific classes of finite groups. This talk is joint work with Bob Oliver. |