If the distinguished basis of a table algebra is an irredundant union of n proper closed subsets, and if the positive structure constants of the quotient table algebra (rescaled to be standard) modulo the intersection of these closed subsets are all at least 1, then it is proved that the order of this quotient algebra is bounded above by a function of n. This generalizes a result of B. H. Neumann for finite groups, applies directly to association schemes, and also yields the following result: if G is a finite group, 𝒦 is the set of ...
