Fusion systems on small p-groups

Abstract: In this article we study several classes of `small' 2-groups: we complete the classification, started in [Stancu, 2006], of all saturated fusion systems on metacyclic p-groups for all primes p. We consider Suzuki 2-groups, and classify all center-free saturated fusion systems on 2-groups of 2-rank 2. We end by classifying all possible F-centric, F-radical subgroups in saturated fusion systems on 2-groups of 2-rank 2.