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arXiv · 2208.04049

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

Marina Anagnostopoulou-Merkouri·Peter J. Cameron
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Abstract

In January 1969, Peter M. Neumann wrote a paper entitled "Primitive permutation groups of degree 3p". The main theorem placed restrictions on the parameters of a primitive but not 2-transitive permutation group of degree three times a prime. The paper was never published, and the results have been superseded by stronger theorems depending on the classification of the finite simple groups, for example a classification of primitive groups of odd degree.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 introduced into the theory of finite permutation groups, and the paper gives a very good summary and application of these techniques. Second, like its predecessor by Helmut Wielandt on primitive groups of degree 2p, it can be re-interpreted as a combinatorial result concerning association schemes whose common eigenspaces have dimensions of a rather limited form. This result uses neither the primality of p nor the existence of a permutation group related to the combinatorial structure. We extract these results and give details of the related combinatorics.

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Marina Anagnostopoulou-Merkouri, Peter J. Cameron. 2022-08-08. Association schemes with given stratum dimensions: on a paper of Peter M. Neumann. https://arxiv.org/abs/2208.04049

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