Fusion systems on maximal class $3$-groups of rank two revisited

TL;DR

This paper completes the classification of saturated fusion systems on maximal class 3-groups of rank two, advancing understanding of their algebraic structure.

Contribution

It provides a comprehensive classification of fusion systems on a specific class of 3-groups, filling a gap in the existing literature.

Findings

Complete classification of fusion systems achieved

Identified unique properties of maximal class 3-groups of rank two

Enhanced understanding of algebraic structures involved

Abstract

We complete the determination of saturated fusion systems on maximal class 3-groups of rank two.