Title: On the composition product of saturated fusion systems

Authors: Sejong Park, Kári Ragnarsson, Radu Stancu

Status: Submitted

Abstract: 
We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. 
We establish a relationship between the characteristic idempotent of a saturated fusion system that is the composition product of saturated subsystems and the characteristic idempotents of the component systems. Consequently we obtain a compatibility result for transfer through the composition product and transfer through the component systems.