Association schemes with given stratum dimensions : on a paper of Peter M. Neumann
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 The paper was never published, and the results have been superseded by stronger theorems depending on the classification of the finite simple groups, for example a classification of primitive groups of odd degree.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.
Citation
Anagnostopoulou-Merkouri , M & Cameron , P J 2023 , ' Association schemes with given stratum dimensions : on a paper of Peter M. Neumann ' , Algebraic Combinatorics , vol. 6 , no. 5 , pp. 1189-1210 . https://doi.org/10.5802/alco.307
Publication
Algebraic Combinatorics
Status
Peer reviewed
ISSN
2589-5486Type
Journal article
Rights
Copyright © The Author(s), 2023. This article is licensed under the Creative Commons Attribution (CC-BY) 4.0 license. http://creativecommons.org/licenses/by/4.0/
Description
Funding: The research of the first author was supported by an Undergraduate Research Bursary, number XCLM18, from the London Mathematical Society. The second author acknowledges the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no. EP/R014604/1), where he held a Simons Fellowship.Collections
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