Title: Fusion systems and amalgams

Authors: Kasper K. S. Andersen, Bob Oliver, Joana Ventura

Abstract:
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 $2$-groups of order at 
most 64, and also reduced fusion systems over $2$-groups having abelian 
subgroups of index two.  More applications are given in later papers.

Status: submitted