Block fusion systems over maximal nilpotency class $3$-groups

TL;DR

This paper extends a key theorem to exotic fusion systems over certain 3-groups, aiming to demonstrate their block exotic nature, which advances understanding of fusion systems in algebra.

Contribution

It generalizes the Reduction Theorem of Kessar-Stancu to apply to exotic fusion systems over maximal nilpotency class 3-groups, a novel theoretical development.

Findings

Extended the Reduction Theorem to new fusion systems

Provided groundwork for proving block exotic properties

Enhanced understanding of fusion systems over nilpotent groups

Abstract

We generalize the Reduction Theorem of Kessar-Stancu so it can be applicable to exotic fusion systems over the maximal nilpotency class of rank two $3$-groups. This is an essential step towards proving that these fusion systems are also block exotic.