Simple fusion system for dihedral group:D8

This article describes a particular fusion system on dihedral group:D8 that turns out to be a simple fusion system: it has no normal fusion subsystems. This is the unique simple fusion system on the group.

Explicit description


For the whole group, the only automorphisms that are included in the fusion system are the inner automorphisms. This can be traced to the fact that the outer automorphism group of the dihedral group is 2-group, and in particular has no 2'-automorphisms.



Fusion of elements
As far as elements are concerned, this fusion system is as rich as possible: any two elements of the same order get fused with each other. Below is some information. Each equivalence class under fusion is presented in terms of its conjugacy classes in the original group: