We define minimal fusion systems in a way that every non-solvable fusion system has a section which is minimal. Minimal fusion systems can also be seen as analogs of Thompsonʼs N-groups. In this paper, we consider a minimal fusion system FF on a finite p-group S that has a unique maximal p -local subsystem containing NF(S)NF(S). For an arbitrary prime p, we determine the structure of a certain (explicitly described) p -local subsystem of FF. If p=2p=2, this leads to a complete classification of the fusion system FF.
- saturated fusion systems
- group theory