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

2021/07/01 by Henke, Ellen
#20D20 #20E25 #20N99 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2107.00305

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 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.

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