Fusion systems of blocks with nontrivial strongly closed subgroups

TL;DR

This paper identifies exotic fusion systems with non-trivial strongly closed subgroups and proves they cannot be realized by p-blocks of finite groups, expanding understanding of fusion system structures.

Contribution

It introduces new exotic fusion systems with non-trivial strongly closed subgroups and demonstrates their non-realizability by finite group p-blocks.

Findings

Existence of exotic fusion systems with non-trivial strongly closed subgroups

Proof that these fusion systems are not realizable by p-blocks of finite groups

Contribution to the classification of fusion systems

Abstract

In this paper, we find some exotic fusion systems which have non-trivial strongly closed subgroups, and we prove these fusion systems are also not realizable by p-blocks of finite groups.