Fusion systems and amalgams
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We study reduced fusion systems from the point of view of their essential subgroups, using the classification by Goldschmidt and Fan of amalgams of prime index to analyze certain pairs of such subgroups. Our results are applied here to study reduced fusion systems over -groups of order at most 64, and also reduced fusion systems over -groups having abelian subgroups of index two. More applications are given in later papers.