Normalizers and centralizers of p-subgroups in normal subsystems of fusion systems

[摘要] Suppose E is a normal subsystem of a saturated fusion system Fover S. If X <= S is fully F-normalized, then Aschbacher defined a normal subsystem N-E(X) of N-F(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 C-E(X) of C-F(X) for every X <= S which is fully F-centralized. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Fusion systems;Localities