A Family of fusion systems related to the groups $\mathrm{Sp}_4(p^a)$ and $\mathrm{G}_2(p^a)$

TL;DR

This paper constructs a family of exotic fusion systems that extend the known fusion systems of Sylow p-subgroups in groups like G_2 and Sp_4, revealing new structures beyond classical groups.

Contribution

It introduces a new family of exotic fusion systems that generalize existing group fusion systems related to G_2 and Sp_4 groups.

Findings

Construction of new exotic fusion systems

Generalization of fusion systems for G_2 and Sp_4

Insights into the structure of Sylow p-subgroups

Abstract

A family of exotic fusion systems generalizing the group fusion systems on Sylow $p$-subgroups of $\mathrm{G}_2(p^a)$ and $\mathrm{Sp}_4(p^a)$ is constructed.