Abstract

Suppose E is a normal subsystem of a saturated fusion system F over S. If X≤S is fully F-normalized, then Aschbacher defined a normal subsystem NE(X) of NF(X). In this short note we revisit and generalize this result using the theory of localities. Our more general approach leads in particular to a normal subsystem CE(X) of CF(X) for every X≤S which is fully F-centralized.

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