Abstract
We prove that an isomorphism between saturated fusion systems over the same finite [Formula: see text]-group is detected on the elementary abelian subgroups of the hyperfocal subgroup if [Formula: see text] is odd, and on the abelian subgroups of the hyperfocal subgroup of exponent at most [Formula: see text] if [Formula: see text]. For odd [Formula: see text], this has implications for mod [Formula: see text] group cohomology.
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