Normal fusion subsystem
From Groupprops
ANALOGY: This is an analogue in fusion system of a property encountered in group. Specifically, it is a fusion subsystem property analogous to the subgroup property: normal subgroup
View other analogues of normal subgroup | View other analogues in fusion systems of subgroup properties (OR, View as a tabulated list)
Definition
A fusion subsystem of a fusion system on a group of prime power order is termed a normal fusion subsystem if:
- The subgroup of for which is a fusion system is a strongly closed subgroup of . In other words, for any with , .
- Conjugation of any morphism in by a morphism in gives a morphism in , in the following sense: If and are morphisms such that is well-defined and between two objects of (i.e., two subgroups of ), then .
References
- Introduction to Fusion Systems by Markus Linckelmann^{Weblink}^{More info}