We offer a sufficient condition for a closed subset in an association scheme to be maximal. The result generalizes naturally the well-known (group-theoretical) fact that the one-point-stabilizer of a flag transitive automorphism group of a 2-design with lambda = 1 must be a maximal subgroup. In finite group theory, there exist a lot of (important) sufficient conditions for a subgroup to be maximal. In the theory of association schemes, the condition which we offer here seems to be the first one which guarantees that a closed subset of the set of relations of an association scheme is maximal. (C) 1997 Academic Press.
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