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In this paper we study the normalizer decomposition of a compact Lie group$G$ using the information of the fusion system $\mathcal{F}$ of $G$ on amaximal discrete $p$-toral subgroup. We prove that there is an injective mapfrom the set of conjugacy classes of chains of $\mathcal{F}$-centric,$\mathcal{F}$-radical discrete $p$-toral subgroups to the set of conjugacyclasses of chains of $p$-centric, $p$-stubborn continuous $p$-toral subgroups.The map is a bijection when $\pi_0(G)$ is a finite $p$-group. We also provethat the classifying space of the normalizer of a chain of discrete $p$-toralsubgroups of $G$ is mod $p$ equivalent to the classifying space of thenormalizer of the corresponding chain of $p$-toral subgroups.

Normalizers of chains of discrete $p$-toral subgroups in compact Lie groups