Fusion systems on small 𝑝-groups

Abstract

In this article we study several classes of ‘small’ 2 2 -groups: we complete the classification, started by Stancu, of all saturated fusion systems on metacyclic p p -groups for all primes p p . We consider Suzuki 2 2 -groups, and classify all center-free saturated fusion systems on 2 2 -groups of 2 2 -rank 2 2 . We end by classifying all possible F \mathcal {F} -centric, F \mathcal {F} -radical subgroups in saturated fusion systems on 2 2 -groups of 2 2 -rank 2 2 .