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We describe a purely group-theoretic condition on an element g of a finitegroup G which implies that g has coefficient zero in every central idempotentelement of the group ring RG, provided that R is a ring of primecharacteristic. We use this condition to prove that the fusion systemassociated to a block of an alternating group is always isomorphic to the groupfusion system of an alternating group.

Block fusion systems of the alternating groups