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Let F be a saturated fusion system over a p-group S and let E be a subsystem of F with AutE(S)=AutF(S). We prove that the fusion system F is generated by all E-morphisms and all F-automorphisms of some domestic intersections (called F∖E-domestic intersections in the paper) of F. We also get some results about control of fusion in finite groups as applications.
Meng et al. (Mon,) studied this question.
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