Existence and uniqueness of components for p-local compact groups

Let $\mathcal{G}=(S,\mathcal{F},\mathcal{L})$ be a $p$-local compact group. An irreducible component is a minimal irreducible $p$-local compact group $\mathcal{G}_0=(S_0,\mathcal{F}_0,\mathcal{L}_0)$ such that $\mathcal{F}_0$ is subnormal in $\mathcal{F}$; a transporter system of components is the corresponding transporter-system structure.

Component uniqueness conjecture. Every $p$-local compact group determines a unique irreducible component and a unique transporter system of components.

The conjecture concerns extending the theory of normal subsystems and quotient localities from finite saturated fusion systems to $p$-local compact groups. Such an extension would provide a systematic notion of components and their transporter systems.