Abstract
Abstract We prove that each exotic fusion system ℱ {\mathcal{F}} on a Sylow p-subgroup of G 2 ( p ) {G_{2}(p)} for an odd prime p with 𝒪 p ( ℱ ) = 1 {\mathcal{O}_{p}(\mathcal{F})=1} is block-exotic. This gives evidence for the conjecture that each exotic fusion system is block-exotic. We prove two reduction theorems for block-realisable fusion systems.
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