Fusion systems on small p-groups

TL;DR

This paper classifies all saturated fusion systems on small 2-groups, including metacyclic and Suzuki 2-groups, and analyzes their subgroup structures, advancing the understanding of fusion systems on small p-groups.

Contribution

It completes the classification of saturated fusion systems on certain small 2-groups, including metacyclic and Suzuki groups, and analyzes subgroup structures.

Findings

Complete classification of saturated fusion systems on metacyclic p-groups.

Classification of all center-free saturated fusion systems on 2-groups of 2-rank 2.

Identification of F-centric, F-radical subgroups in these systems.

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.