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no. 5
Association schemes with given stratum dimensions: on a paper of Peter M. Neumann
Anagnostopoulou-Merkouri, Marina1; Cameron, Peter J.2
1 School of Mathematics University of Bristol Bristol BS8 1QU UK
2 School of Mathematics and Statistics University of St Andrews St Andrews Fife KY16 9SS UK
Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1189-1210.

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 The paper was never published, and the results have been superseded by stronger theorems depending on the classification of the finite simple groups, for example a classification of primitive groups of odd degree.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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.307
Classification: 05E30, 20B15
Keywords: association scheme, permutation group, strongly regular graph

Anagnostopoulou-Merkouri, Marina 1; Cameron, Peter J. 2

1 School of Mathematics University of Bristol Bristol BS8 1QU UK
2 School of Mathematics and Statistics University of St Andrews St Andrews Fife KY16 9SS UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Anagnostopoulou-Merkouri, Marina; Cameron, Peter J. Association schemes with given stratum dimensions: on a paper of Peter M. Neumann. Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1189-1210. doi : 10.5802/alco.307. https://alco.centre-mersenne.org/articles/10.5802/alco.307/

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