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In January 1969, Peter M. Neumann wrote a paper entitled "Primitivepermutation groups of degree 3p". The main theorem placed restrictions on theparameters of a primitive but not 2-transitive permutation group of degreethree times a prime. The paper was never published, and the results have beensuperseded by stronger theorems depending on the classification of the finitesimple groups, for example a classification of primitive groups of odd degree.  However, there are further reasons for being interested in this paper. First,it was written at a time when combinatorial techniques were being introducedinto the theory of finite permutation groups, and the paper gives a very goodsummary and application of these techniques. Second, like its predecessor byHelmut Wielandt on primitive groups of degree 2p, it can be re-interpreted as acombinatorial result concerning association schemes whose common eigenspaceshave dimensions of a rather limited form. This result uses neither theprimality of p nor the existence of a permutation group related to thecombinatorial structure. We extract these results and give details of therelated combinatorics.

Association schemes with given stratum dimensions: on a paper of Peter M. Neumann